Inclusion Criteria:

• Participants must be able to give self-consent and then sign and date an IRB/Independent Ethics Committee (IEC)-approved written informed consent in accordance with regulatory and institutional guidelines. This must be obtained before the performance of any protocol related procedures that are not considered part of normal patient care.
• Participants must be willing and able to comply with scheduled visits, treatment schedule, laboratory testing, and other requirements of the study.
• Participants must provide consent for mandatory tumor biopsy samples.
• All participants must have inoperable, advanced, or metastatic EC, GC or GEJ carcinoma and have histologically confirmed predominant adenocarcinoma and/or squamous carcinoma. The documentation of GEJ involvement can include biopsy, endoscopy, or imaging.
• Participants with human epidermal growth factor receptor 2 (HER2) overexpressing tumor who progress after trastuzumab (or are ineligible for or unwilling to be treated with trastuzumab) are eligible to be enrolled.
• Prior adjuvant or neoadjuvant chemotherapy, radiotherapy, and/or chemoradiotherapy are permitted, as long as the last administration of the last regimen (whichever was given last) occurred at least 4 weeks prior to randomization.
• Participants must have an Eastern Cooperative Oncology Group performance status ≤ 1.
• Track-specific eligibility criteria:
  • Track 1: anti-PD-1, anti-PD-L1, and anti-CTLA-4 treatment-naïve participants:
    • Participants must not have received any anti-PD-1, anti-PD-L1, or anti-CTLA-4 treatment prior to this study. Participants previously treated with agents other than anti-PD-1, anti-PD-L1, or anti-CTLA-4 are eligible for Track 1;
    • Participants may have been offered platinum-based chemotherapy for progressive or recurrent disease.
      • The platinum-based chemotherapy may have been in the adjuvant, neoadjuvant, or recurrent setting.
• All Subjects must consent to the acquisition of fresh pre- and on-treatment tumor biopsies for performance of correlative biomarker studies. Archival specimens may not be substituted for fresh baseline specimens but can be submitted  to help understand the evolution of the tumor (i.e., PD-L1 expression changes over time) for performance of correlative studies. Subjects who either do not consent to a pretreatment tumor biopsy or do not have accessible lesions are not eligible. An adequate baseline tumor biopsy as determined by a central laboratory pathologist must be obtained prior to randomization. If fresh biopsy is not clinically feasible or safe, the option of archival tissue can be discussed  with BMS if the biopsy was obtained within 90 days of study enrollment and there was no intervening systemic anticancer or IO therapy.
• Track 2: anti-PD-1, anti-PD-L1, or anti-CTLA-4 treatment-experienced participants:
  • Participants must have had progressive or recurrent disease during or after anti-PD-1, anti-PD-L1, or anti-CTLA-4 treatment. (Participants treated with any study treatment targeting PD-1, PD-L1, or CTLA-4 will be considered anti-PD-1, anti-PD-L1, or anti-CTLA-4 treatment experienced, respectively);
  • Participants may have been offered platinum-based chemotherapy for GC or GEJ;
    • The platinum-based chemotherapy may have been in the adjuvant, neoadjuvant, or recurrent setting.
  • Participants who have had prior treatment with any 1 of the agents (or any other agent targeting PD-1, PD-L1, or CTLA-4) in monotherapy or in any combination regimen in a FRACTION-Gastric Cancer Sub-Protocol are eligible for treatment on Track 2;
  • Participants who have had prior combination treatment with the same IO combination agents (or IO agents directed against the same targets) as 1 of the combination regimens in a FRACTION-Gastric Cancer Sub-Protocol are eligible for study treatment on Track 2 but must be randomized to another combination regimen.
• All Subjects must consent to the acquisition of fresh pre- and on-treatment tumor biopsies for performance of correlative biomarker studies. Archival specimens may not be substituted for fresh baseline specimens but can be submitted to help understand the evolution of the tumor (ie, PD-L1 expression changes over time) for performance of correlative studies. Subjects who either do not consent to a pretreatment tumor biopsy or do not have accessible lesions are not eligible. An adequate baseline tumor biopsy as determined by a central laboratory pathologist must be obtained prior to randomization. If fresh biopsy is not clinically feasible or safe, the option of archival tissue can be discussed with BMS if the biopsy was obtained within 90 days of study enrollment and there was no intervening systemic anticancer or IO therapy.
• At the time of screening, participants must have a life expectancy of at least 3 months following their most recent chemotherapy or immunotherapy for entry into all tracks.
  • Participants who wish to be re-randomized to a new study treatment combination on Track 2 following progression on a prior study treatment in Tracks 1 or 2 must have a life expectancy of at least 3 months following the last study treatment.
• Participants receiving prior palliative radiotherapy to a non-central nervous system (CNS) lesion must have completed that treatment at least 2 weeks prior to the first dose of study treatment.
  • Participants with symptomatic tumor lesions at baseline who may require palliative radiotherapy within 4 weeks of the first dose of study treatment are strongly encouraged to receive palliative radiotherapy prior to  enrollment, and they must complete that treatment at least 2 weeks prior to the first dose of study treatment.
• Participants must have at least 1 lesion with measurable disease, as defined by RECIST v1.1 criteria for solid tumors response assessment.
  • Participants with lesions in a previously irradiated field as the sole site of measurable disease will be permitted to enroll, provided that the lesion(s) have demonstrated clear progression and can be measured accurately.
• Participants with toxicity from any prior anti-cancer treatment must have their toxicity returned to Grade ≤ 1 (NCI CTCAE Version 4.03) or baseline before administration of study treatment.
  • Participants with Grade ≥ 2 toxicities attributed to prior anti-cancer treatment that are not expected to resolve and result in long-lasting sequelae, such as neuropathy after a platinum based- treatment, are eligible;
  • Grade > 1 alopecia or fatigue is permitted.
• Participants must allow a tumor biopsy at the following time points:
  • baseline (prior to study treatment); 
  • on-study (Day 28 ontreatment); and
  • EOT, defined as at the time of progression or at the time of a clinically significant event (e.g., at EOT for participants with PR or SD or at EOT for participants who discontinue treatment due to an AE), provided that the biopsy is at acceptable clinical risk as judged by the investigator for each study treatment regimen to:  1) identify predictive biomarkers for both safety and efficacy of a given combination, 2) define the mechanism of action for a particular combination (pharmacodynamic assessment), and 3) determine the mechanisms of resistance to a particular combination.
• Participants who do not have accessible or suitable lesions are not eligible.
  • Baseline biopsies may be collected from participants with a single measureable lesion (primary or metastatic), as long as it is not an excisional biopsy.
• For participants whose pretreatment biopsy yields inadequate tissue quantity or quality (as determined by a pathologist in the central laboratory), re-biopsy is permitted.
• The solid tumor tissue specimen must be a core-needle, biopsy or an excisional or incisional biopsy. Fine-needle biopsies and drainage of pleural effusions with cytospins are not considered adequate for biomarker review and randomization. Biopsies of bone lesions that do not have a soft tissue component or decalcified bone tumor samples are also not acceptable.
  • Punch biopsies are acceptable as long as adequate tumor material is provided.
• The biopsy at progression of disease after treatment on any track may function as the pretreatment biopsy for subsequent treatment on Track 2.
• Study personnel must ensure that the archival tissue block (preferred) or slides samples, if available, are located and shipped to the central laboratory prior to randomization within 6 weeks of signing the written informed consent, as long as this tissue will not be used for the screening biopsy sample.
• Participants must have adequate organ function, as defined by the following:
  • White blood cells ≥ 2,000/μL (stable off any growth factor after discontinuation within 2 weeks of the first study treatment administration);
  • Neutrophils ≥ 1,500/μL (stable off any growth factor after discontinuation within 2 weeks of the first study treatment administration);
  • Platelets ≥ 100 x 103/μL (transfusion to achieve this level is not permitted within 2 weeks of the first study treatment administration);
  • Hemoglobin ≥ 9.0 g/dL (transfusion to achieve this level is not permitted within 2 weeks of the first study treatment administration);
  • Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 3 x institutional upper limit of normal (ULN);
  • Total bilirubin ≤ 1.5 x institutional ULN (except for participants with Gilbert’s syndrome who must have normal direct bilirubin);
  • Serum creatinine ≤ 1.5 x institutional ULN or creatinine clearance (CrCl)  ≥ 40 mL/min (measured using the Cockcroft-Gault formula below):
    • Female CrCl = (140 - age in years) x weight in kg x 0.85
                                72 x serum creatinine in mg/dL
    • Male CrCl = (140 - age in years) x weight in kg x 1.00
                              72 x serum creatinine in mg/dL
• Participants must be able to comply with restrictions and prohibited activities/treatments.
• Participant re-enrollment: This study permits the re-enrollment of a participant who has discontinued the study as a pretreatment failure (e.g., participant has not been treated). If re-enrolled, the participant must be re-consented.
• Participants must allow a tumor biopsy at baseline and on study.
  • Participants who do not have accessible or suitable lesions are not eligible.
  • For participants whose pretreatment biopsy yields inadequate tissue quantity or quality (as determined by a pathologist in the central laboratory), re-biopsy is permitted.
  • The solid tumor tissue specimen must be a core-needle, biopsy or an excisional or incisional biopsy. Fine-needle biopsies and drainage of pleural effusions with cytospins are not considered adequate for biomarker review and randomization. Biopsies of bone lesions that do not have a soft tissue component or decalcified bone tumor samples are also not acceptable.
    • Punch biopsies are acceptable as long as adequate tumor material is provided.
• The biopsy at progression of disease after treatment on any track may function as the pretreatment biopsy for subsequent treatment on Track 2.
• Males and females, ages 18 years or older at the time of consent
• Women of child-bearing potential (WOCBP) must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin) within 24 hours prior to the start of study treatment. An extension up to 72 hours prior to the start of study treatment is permissible in situations where results cannot be obtained within the standard 24-hour window.
• Women must not be breastfeeding.
• WOCBP must agree to follow instructions for method(s) of contraception for the duration of treatment with study treatment(s) plus the time required for the study treatment to undergo approximately 5 half-lives, plus the duration of 1 ovulatory cycle (30 days), for a total of 5 months posttreatment completion. If the half-life of a study treatment in a FRACTION-Gastric Cancer Sub-Protocol is longer than approximately 5 half-lives of nivolumab, this will be addressed in the FRACTION-Gastric Cancer Sub-Protocol.
  • WOCBP who are continuously not heterosexually active are also exempt from contraceptive requirements and still must undergo pregnancy testing, as described in this section.
• Males who are sexually active with WOCBP must agree to follow instructions for method(s) of contraception and fetal protection for the duration of treatment with study treatment(s) plus approximately 5 half-lives of the study treatment, plus the duration of sperm turnover (90 days), for a total of 7 months post-treatment completion. In addition, male participants must be willing to refrain from sperm donation during this time.
  • Azoospermic males are exempt from contraceptive requirements.
• Investigators shall counsel WOCBP and male participants who are sexually active with WOCBP on the importance of pregnancy prevention and the implications of an unexpected pregnancy and when applicable, the potential of fetal toxicity occurring due to transmission of study drug, present in seminal fluid, to a developing fetus, even if the participant has undergone a successful vasectomy or if the partner is pregnant. Investigators shall advise on the use of highly effective methods of contraception, which have a failure rate of < 1% when used consistently and correctly.

Exclusion Criteria:

• Participants with HER2-positive tumor and previously untreated with trastuzumab are excluded; participants who are ineligible for or unwilling to be treated with trastuzumab are still eligible.
• Participants with ascites that cannot be controlled with appropriate interventions.
• Participants must not have suspected, known, or progressive CNS metastases; have untreated CNS metastases; or have the CNS as the only site of disease.
  • Participants are eligible if CNS metastases are adequately treated and participants neurologically return to baseline (except for residual signs or symptoms related to the CNS treatment) for at least 2 weeks prior to study entry. In addition, participants must be either off corticosteroids or on a stable or decreasing dose of prednisone ≤ 10 mg daily (or equivalent) for at least 2 weeks prior to study entry;
  • Participants must not have leptomeningeal disease or carcinomatous meningitis.
• Participants must not have prior malignancy active within the previous 3 years except for locally curable cancers that have been apparently cured, such as basal or squamous cell skin cancer, superficial bladder cancer, or carcinoma in situ of the prostate, cervix, or breast.
• Participants must not have other active malignancy requiring concurrent intervention.
• Participants must not have received a prior organ allograft.
• Participants must not have received any anti-cancer treatment (e.g., chemotherapy or radiotherapy [except for palliative radiotherapy, which can be received at least 2 weeks prior to study treatment]; biologics; or immunotherapies, including investigational treatments) within 4 weeks prior to the first dose of study treatment administration.
• Participants who have received noncytotoxic anti-cancer therapies (e.g., prior use of targeted treatment) and who have completed treatment at least 4 weeks or 5 half-lives (whichever is shorter) prior to the first dose of study treatment are eligible to enroll.  However, if 5 half-lives is shorter than 4 weeks, agreement with the BMS Medical Monitor (or designee) is mandatory.
• Participants must not have active, known, or suspected autoimmune disease.
  • Participants with type I diabetes mellitus, hypothyroidism only requiring hormone replacement treatment, skin disorders (such as vitiligo, psoriasis, or alopecia) not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll.
• Participants must not have a condition requiring systemic treatment with either corticosteroids (prednisone > 10 mg daily or equivalent) or other immunosuppressive medications within 14 days of study treatment administration.
  • Inhaled or topical steroids and adrenal replacement steroid (prednisone > 10 mg daily or equivalent) are permitted in the absence of active autoimmune disease.
• Participants must not have a history of life-threatening toxicity related to prior IO treatment (e.g., anti-CTLA-4 or anti-PD-1/PD-L1 treatment or any other antibody or treatment specifically targeting T-cell co-stimulation or immune checkpoint pathways).
• Participants with toxicities that are unlikely to recur with standard countermeasures (e.g., hormone replacement treatment after adrenal crisis) are eligible.
• Participants must not have interstitial lung disease that is symptomatic or may interfere with the detection or management of suspected treatment-related pulmonary toxicity.
• Participants must not have uncontrolled or significant cardiovascular disease including, but not limited to, any of the following:
  • Myocardial infarction or stroke/transient ischemic attack within the past 6 months;
  • Uncontrolled angina within the past 3 months;
  • Any history of clinically significant arrhythmias (such as ventricular tachycardia, ventricular fibrillation, or torsades de pointes);
  • QT interval corrected with Fridericia’s formula ≥ 480 ms;
  • History of other clinically significant heart disease (e.g., cardiomyopathy, congestive heart failure with New York Heart Association functional classification III to IV, myocarditis, pericarditis, or significant pericardial effusion).
• Participants who require daily supplemental oxygen treatment are excluded.
• Participants must not have any positive test result for hepatitis B virus or hepatitis C virus (HCV) indicating presence of virus, for example, hepatitis B surface antigen (Australia antigen) positive or hepatitis C antibody (anti-HCV) positive (except if HCV-ribonucleic acid [RNA] negative).
• Participants with a history of resolved hepatitis A virus infection are eligible.
• Participants must not have evidence of active infection requiring antibacterial, antifungal, or antiviral treatment ≤ 7 days prior to initiation of study treatment.
• Participants must not have a known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome.
• Testing for HIV must be performed at sites mandated by local requirements. 
• Participants must not have known or suspected active tuberculosis.
• Participants must not have had any major surgery within 4 weeks of study treatment administration. Participants must have recovered from the effects of a major surgery or significant traumatic injury at least 14 days before the first dose of study treatment.
• Participants must not have received nononcology vaccines containing live virus for prevention of infectious diseases within 12 weeks prior to the first dose of study treatment.
  • The use of inactivated seasonal influenza vaccines (e.g., Fluzone®) will be permitted on study without restriction.
• Participants must not have received packed red blood cell or platelet transfusion within 2 weeks prior to the first dose of study treatment.
• Participants must not have a known or underlying serious or uncontrolled medical condition that, in the opinion of the investigator or Sponsor, could make the administration of study treatment hazardous to the participants or could adversely affect the ability of the participant to comply with or tolerate the study.
• History of any significant treatment allergy (such as anaphylaxis or hepatotoxicity) to prior anti-cancer immune-modulating therapies (e.g., checkpoint inhibitors and T-cell co-stimulatory antibodies).
• History of allergy or hypersensitivity to study treatment components.
• Prisoners or participants who are involuntarily incarcerated.
  • Note: Under certain specific circumstances, and only in countries where local regulations permit, a person who has been imprisoned may be included or permitted to continue as a participant. Strict conditions apply, and BMS approval is required.
• Participants who are compulsorily detained for treatment of either a psychiatric or physical (e.g., infectious disease) illness.

Eligibility criteria for this study have been carefully considered to ensure the safety of the study participants and that the results of the study can be used. It is imperative that participants fully meet all eligibility criteria.