Inclusion Criteria:

• Are ≥ 18 (or ≥ 20 in Japan and Taiwan or age legally considered to be an adult) years of age at the time of signing the informed consent. In Japan, a participant aged < 20 years of age but ≥ 18 years of age may participate if written informed consent from his/her parent or guardian is provided in addition to the participant’s written informed consent.
• Are participants with histologically or cytologically confirmed locally advanced or metastatic BTC, including intrahepatic CCA, extrahepatic CCA, gallbladder cancer, and ampulla of Vater’s cancer. The histological origin of ampullary carcinomas (intestinal, pancreaticobiliary, or other) will be collected. Histological subtypes such as a sarcomatoid tumor or HCC mixed subtype, for which- gemcitabine and cisplatin treatment are not considered as the standard of care should be excluded. Contact Medical Monitor for rare subtypes.
• Naïve to chemotherapy, immunotherapy, and interventional radiological treatment (transarterial chemo-embolization, transarterial embolization, transarterial infusion) for locally advanced or metastatic BTC. Participants whose disease has recurred ≥ 6 months after completion of neoadjuvant or adjuvant treatments will be considered eligible.
• Availability of tumor tissue (primary or metastatic) (fresh or archival biopsies) before the first administration of study intervention. Availability of tumor tissue is mandatory except for the safety run-in part. Brush cytology and cell blocks are not acceptable. Tumor tissue (fresh or archival) must be suitable for biomarker assessment as described in the Laboratory Manual.
• At least 1 measurable lesion according to RECIST 1.1. Participants in the safety run-in part do not require a measurable lesion at baseline.
• ECOG PS of 0 or 1 at study entry and at Week 1, Day 1 prior to dosing.
• Life expectancy of ≥ 12 weeks, as judged by the Investigator.
• Adequate hematological function defined by white blood cell count ≥ 2.0 × 10^9 /L with absolute neutrophil count ≥ 1.5 × 10^9 /L, lymphocyte count ≥ 0.5 × 10^9 /L, platelet count ≥ 100 × 10^9 /L, and hemoglobin (Hgb) ≥ 9 g/dL (participants may have been transfused) at study entry and at Week 1 Day 1 prior to dosing.
• Previously transfused participants are allowed in the study with a stable Hgb of ≥ 9 g/dL at the time of study entry.
• Adequate hepatic function defined by a total bilirubin level ≤ 1.5 × upper limit of normal (ULN), an aspartate aminotransferase level ≤ 3.0 × ULN, and an alanine aminotransferase level ≤ 3.0 × ULN. For participants with liver involvement, aspartate aminotransferase ≤ 5.0 × ULN and alanine aminotransferase ≤ 5.0 × ULN are acceptable.
• Adequate renal function defined by an estimated creatinine clearance (CrCl) > 50 mL/min according to the Cockcroft-Gault formula or by measure of CrCl from 24-hour urine collection.
• CrCl (mL/min) = (140-age) × weight (kg) / (72 × serum creatinine | If female, × 0.85;
• If creatinine is measured by the enzymatic method, add 0.2 and use as Crjaffe = 0.2 + Crenzyme.
• Albumin ≥ 2.8 g/dL.
• Adequate coagulation function defined as prothrombin time or international normalized ratio ≤ 1.5 × ULN unless the participant is receiving anticoagulant therapy.
• Hepatitis B virus (HBV) deoxyribonucleic acid (DNA) positive participants must be treated and on a stable dose of antivirals (e.g., entecavir, tenofovir, or lamivudine; adefovir or interferon is not allowed) at study entry and with planned monitoring and management including baseline HBV DNA quantity according to appropriate labeling guidance. Participants receiving active hepatitis C virus (HCV) therapy must be on a stable dose at study entry and with planned monitoring and management according to appropriate labeling guidance of approved antiviral.
• Are male or female.
• Male participants agree to the following during the intervention period and for at least 4 months after the last dose of study intervention (35 days corresponding to the time needed to eliminate any study interventions, e.g., 5 terminal half-lives plus 90 days for spermatogenic cycle):
  • Refrain from donating sperm PLUS, either:
  • Abstain from any activity that allows for exposure to ejaculate; OR
  • Use a male condom: When having sexual intercourse with a woman of childbearing potential who is not currently pregnant, and advise her to use a highly effective contraceptive method with a failure rate of < 1% per year, since a condom may break or leak;
  • When engaging in any activity that allows for exposure to ejaculate.
  • Female participants are not pregnant or breastfeeding, and at least 1 of the following conditions applies:
    • Not a woman of childbearing potential; OR
  • If a woman of childbearing potential, agree to use a highly effective contraceptive method (i.e., with a failure rate of < 1% per year), preferably with low user dependency, for the following time periods:
  • Before the first dose of study intervention(s), if using hormonal contraception:
  • Has completed at least one 4-week cycle of an oral contraceptive pill and has either had or has begun her menses; OR
  • Has used a depot contraceptive or extended-cycle contraceptive for at least 28 days and has a documented negative pregnancy test using a highly sensitive assay;
  • During the intervention period;
  • After the study intervention period (i.e., after the last dose of study intervention is administered) for at least 65 days (time needed to eliminate any study interventions; e.g., 5 terminal half-lives plus 30 days for a menstrual cycle), and as indicated in the respective label (Summary of Product Characteristics [SmPC]) for gemcitabine and cisplatin. Participants have to agree to the followings:
  • Women of childbearing potential should refrain from donating eggs from the start of dosing until 2 months after discontinuing study intervention.
  • The Investigator evaluates the effectiveness of the contraceptive method in relationship to the first dose of study intervention.
  • Have a negative serum or highly sensitive urine pregnancy test, as required by local regulations, within 24 hours before the first dose of study intervention. If a urine test cannot be confirmed as negative (e.g., an ambiguous result), a serum pregnancy test is required.
  • The Investigator reviews the medical history, menstrual history, and recent sexual activity to decrease the risk for inclusion of a female with an early, undetected pregnancy.
• Capable of giving signed informed consent which includes compliance with the requirements and restrictions listed in the Informed Consent Form (ICF) and this protocol.

Exclusion Criteria:

• Previous and/or intercurrent cancers. With the exception of: curatively-treated cancers with no recurrence in > 3 years or early cancers treated with curative intent, including but not limited to cervical carcinoma in situ, superficial, noninvasive bladder cancer, basal cell carcinoma, squamous cell carcinoma in situ, or endoscopically resected gastrointestinal cancers limited in mucosal layer.
• Rapid clinical deterioration not related to malignancy which, in the opinion of the Investigator, may predispose to inability to tolerate treatment or study procedures at study entry and at Week 1 Day 1 prior to dosing.
• Participants with symptomatic central nervous system (CNS) metastases are excluded. Participants with a history of treated CNS metastases (by surgery or radiation therapy) are not eligible unless they are judged to have fully recovered from treatment.
• Receipt of any organ transplantation, including allogeneic stem-cell transplantation, but with the exception of transplants that do not require immunosuppression (e.g., corneal transplant, hair transplant).
• Significant acute or chronic infections including:
  • Known history of positive test for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (testing at Screening is not required). If an Investigator has a strong suspicion of HIV infection without known history for a participant in screening, but the participant refuses testing, discuss with Medical Monitor to assess eligibility.
  • Note: HIV testing is not mandated for study inclusion; however, if it is performed at any point in screening or while on study, a site must consent the participant for HIV testing as per local standard guidance.
  • Active tuberculosis (presence of clinical symptoms, physical or radiographic findings of active tuberculosis);
  • Uncontrolled biliary infection. Biliary tract obstruction should be released by stenting or percutaneous transhepatic biliary drainage (PTBD). Participants with biliary obstruction should have adequate biliary drainage with no evidence of ongoing infection without antibiotics treatment during the screening period;
  • Active bacterial, fungal, or viral infection (with the exception of hepatitis B and hepatitis C) requiring systemic therapy during the screening period.
• Active autoimmune disease that might deteriorate when receiving an immunostimulatory agent:
  • Participants with type 1 diabetes, vitiligo, alopecia, psoriasis, hypo- or hyperthyroid disease not requiring immunosuppressive treatment are eligible;
  • Participants requiring hormone replacement with corticosteroids are eligible if the steroids are administered only for the purpose of hormonal replacement and at doses ≤ 10 mg of prednisone or equivalent per day;
  • Administration of steroids for other conditions through a route known to result in a minimal systemic exposure (topical, intranasal, intra-ocular, or inhalation) is acceptable.
• History of, or concurrent, interstitial lung disease.
• Known history of hypersensitivity reactions to bintrafusp alfa or its products or known severe hypersensitivity reactions to monoclonal antibodies (Grade ≥ 3 National Cancer Institute [NCI]-Common Terminology Criteria for Adverse Events [CTCAE] Version 5.0), any history of anaphylaxis, or recent (within 5 months) history of uncontrolled asthma.
• Clinically significant cardiovascular/cerebrovascular disease as follows: cerebral vascular accident/stroke (< 6 months prior to enrollment), myocardial infarction (< 6 months prior to enrollment), unstable angina, congestive heart failure (New York Heart Association Classification ≥ Class II), or serious cardiac arrhythmia.
• Other severe, acute, or chronic medical conditions, including immune colitis, inflammatory bowel disease, immune pneumonitis, or psychiatric conditions, including recent (within the past year) or active suicidal ideation or behavior. Participants with history of bleeding diathesis or recent major bleeding events considered by the Investigator as high risk for study intervention are also excluded.
• Chronic obstructive pulmonary disease exacerbation or other respiratory illness requiring hospitalization or precluding study therapy within 30 days before randomization.
• Participants who are candidates for liver transplantation and who can receive the transplantation within a medically acceptable period.
• Concurrent treatment with nonpermitted drugs. Participants who have completed prior adjuvant therapy ≥ 6 months prior to randomization are eligible.
• Prior therapy with any antibody/drug targeting T-cell coregulatory proteins (immune checkpoints), including but not limited to anti-PD-1, anti-PD-L1, anti-cytotoxic T-lymphocyte-associated antigen 4 (CTLA-4) antibody, or anti-4-1BB antibody is not allowed, inclusive of localized administration of such agents.
• Prior therapy with any antibody/drug targeting TGFβ/TGFβ receptor.
• Radiation within 28 days other than focal palliative bone-directed radiotherapy.
• Systemic therapy with immunosuppressive agents within 7 days before the start of study intervention; or use of any investigational drug within 28 days before the start of study intervention.
• Live vaccine administration within 4 weeks of study intervention administration.
• Participation in any concurrent interventional clinical study.
• Participation in any concurrent interventional clinical study.
• Major surgery within 28 days before the start of study intervention (excluding prior diagnostic biopsy and stenting/PTBD for the purpose of releasing biliary tract obstruction).
• Pregnancy or breastfeeding.
• Known alcohol or drug abuse.
• Legal incapacity or limited legal capacity.