Inclusion Criteria: 

• Ability to comprehend and willingness to sign a written ICF for the study.
• Men and women 18 years of age or older (or as applicable per local country requirements).
• Confirmed diagnosis of locally advanced or metastatic SCAC.
• Participants must have had progression on or after platinum-based therapy unless ineligible for or intolerant of platinum.
  • No more than 2 prior lines of systemic therapy for metastatic disease are permitted;
  • Participants who are ineligible for platinum must have received at least 1 prior line of systemic therapy;
  • Participants receiving platinum-based radiosensitizing chemotherapy are eligible if relapse occurs < 6 months from completion of treatment.
• Must have measurable disease by RECIST v1.1.
• ECOG performance status 0 to 1.
• If a participant is known to be HIV-positive, then all of the following criteria must also
• be met:
  • CD4+ count ≥ 300/μL;
  • Undetectable viral load;
  • Receiving antiretroviral therapy (ART).
• Willingness to avoid pregnancy or fathering children based on the criteria below.
  • a. Men must agree to take appropriate precautions to avoid fathering children (with at least 99% certainty) from screening through 6 months after the last dose of study drug (or longer as appropriate based on country-specific requirements) and must refrain from donating sperm during this period. Permitted methods that are at least 99% effective in preventing pregnancy (see Appendix A) should be communicated to the participants and their understanding confirmed.
  • Women of childbearing potential must have a negative serum pregnancy test at screening and must agree to take appropriate precautions to avoid pregnancy (with at least 99% certainty) from screening through 6 months after the last dose of study drug. Permitted methods that are at least 99% effective in preventing pregnancy should be communicated to the participants and their understanding confirmed.
  • Women of nonchildbearing potential (ie, surgically sterile with a hysterectomy and/or bilateral oophorectomy OR ≥ 12 months of amenorrhea and at least 50 years of age) are eligible.
• Participants known to be HIV-positive are eligible to enter the translational substudy, which requires the participant to sign a separate ICF, and the participant must be willing and able to provide additional tissue and blood samples.

Exclusion Criteria: 

• Receipt of anticancer therapy or participation in another interventional clinical study within 21 days before the first administration of study drug; 6 weeks for mitomycin C.
• Radiotherapy within 14 days of first dose of study treatment with the following caveats:
  • 28 days for pelvic radiotherapy.
  • 6 months for thoracic region radiotherapy that is > 30 Gy in 2 Gy fractions.
• Prior treatment with PD-1 or PD-L1 directed therapy (other immunotherapies may be acceptable with prior approval from the medical monitor).
• Toxicity of prior therapy that has not recovered to ≤ Grade 1 or baseline (with the exception of any grade of alopecia and anemia not requiring transfusion support).
• Endocrinopathy, if well-managed, is not exclusionary and should be discussed with sponsor medical monitor.
• Participants with laboratory values at screening below:
• Hematology
  • Platelets ≤ 75 × 109/L
  • Hemoglobin ≤ 9 g/dL
  • ANC ≤ 1.5 × 109/L
• Hepatic
  • ALT > 2.5 × ULN OR > 5 × ULN for participants with liver metastases
  • AST > 2.5 × ULN OR > 5 × ULN for participants with liver metastases
  • Bilirubin ≥ 1.5 × ULN unless conjugated bilirubin ≤ULN (conjugated bilirubin only needs to be tested if total bilirubin exceeds ULN). If there is no institutional ULN, then direct bilirubin must be < 40% of total bilirubin.
• Renal
  • Calculated creatinine clearance < 30 mL/min
• Coagulation
  • INR or PT > 1.5 × ULN, for participants not receiving anticoagulant therapy
  • aPTT > 1.5 × ULN for participants not receiving anticoagulant therapy
• Known additional malignancy that is progressing or requires active treatment, or history of other malignancy within 3 years of study entry with the exception of cured basal cell or squamous cell carcinoma of the skin, superficial bladder cancer, prostate intraepithelial neoplasm, carcinoma in situ of the cervix, or other noninvasive or indolent malignancy, or cancers from which the participant has been disease-free for > 1 year, after treatment with curative intent.
• Active autoimmune disease requiring systemic immunosuppression in excess of physiologic maintenance doses of corticosteroids (> 10 mg of prednisone or equivalent).
• Evidence of interstitial lung disease or active noninfectious pneumonitis.
• Known active CNS metastases and/or carcinomatous meningitis.
  • Note: Participants with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least 28 days before the first dose of study drug and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases or CNS edema, and have not required steroids for at least 14 days before the first dose of study drug.
• Known active HAV, HBV, or HCV infection, as defined by elevated transaminases with the following serology: positivity for HAV IgM antibody, anti-HCV, anti-HBc IgG or IgM, or HBsAg (in the absence of prior immunization).
• Active infections requiring systemic therapy.
• Known hypersensitivity to another monoclonal antibody that cannot be controlled with standard measures (e.g., antihistamines and corticosteroids) or known allergy or hypersensitivity to any component of INCMGA00012 or formulation components.
• Participants with impaired cardiac function or clinically significant cardiac disease:
  • New York Heart Association Class III or IV cardiac disease, including preexisting clinically significant ventricular arrhythmia, congestive heart failure, or cardiomyopathy;
  • Unstable angina pectoris;
  • Acute myocardial infarction ≤ 6 months before study participation;
  • Other clinically significant heart disease (i.e., ≥ uncontrolled Grade 3 hypertension).
• Participant is pregnant or breastfeeding.
• Participant is expecting to conceive or father children within the projected duration of the study, from screening through 6 months after the last dose of study drug.
• Participant has not recovered adequately from toxicities and/or complications from surgical intervention before starting study drug.
• Has received a live vaccine within 28 days of the planned start of study drug.
  • Note: Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, chicken pox/zoster, yellow fever, rabies, BCG, and typhoid vaccine.  Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (eg, FluMist®) are live-attenuated vaccines and are not allowed.
• Current use of prohibited medication.
• Any condition that would, in the investigator's judgment, interfere with full participation in the study, including administration of study drug and attending required study visits; pose a significant risk to the participant; or interfere with interpretation of study data.