A Phase II Study of Single Tremelimumab With Regular Interval Durvalumab Plus Gemcitabine and Cisplatin in Locally Advanced Unresectable/Metastatic Combined Hepatocellular-cholangiocarcinoma

Inclusion Criteria: 1. Capable of giving signed informed consent which includes compliance with the requirements and restrictions listed in the informed consent form (ICF) and in this protocol. Written informed consent and any locally required authorization (e.g., Health Insurance Portability and Accountability Act in the US, European Union \[EU\] Data Privacy Directive in the EU) obtained from the subject/legal representative prior to performing any protocol-related procedures, including screening evaluations. Informed written consent must be ≤ 28 days prior to registration. 2. Age ≥ 18 years at the time of registration. 3. Body weight \> 30 kg. 4. Histological or cytological confirmation of combined hepatocellular-cholangiocarcinoma. NOTE: Locally advanced unresectable/metastatic. 5. Measurable disease according to RECIST 1.1. NOTE: See Section 9 for additional details. 6. Must have life expectancy ≥ 12 weeks. 7. Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 or 1 within 28 days prior to registration. 8. Adequate organ and marrow function as defined below. All screening labs to be obtained ≤ 28 days prior to registration. * Absolute neutrophil count (ANC) ≥ 1,500/mm3 * Platelet count ≥ 100,000/mm3 * Hemoglobin ≥ 9.0 g/dL * Total Bilirubin ≤ 1.5 x upper limit of normal (ULN). NOTE: This will not apply to subjects with confirmed Gilbert's syndrome (persistent or recurrent hyperbilirubinemia that is predominantly unconjugated in the absence of hemolysis or hepatic pathology), who will be allowed only in consultation with their physician and with a Total Bilirubin \< 3 x ULN. * Alanine aminotransferase (ALT) and aspartate transaminase (AST) ≤ 2. 5 x ULN unless liver metastases are present, in which case it must be ≤ 5 x ULN * PT and INR and aPTT ≤ 1.5 x ULN. NOTE: If patient is receiving anticoagulant therapy and INR or aPTT is within target range of therapy subject is eligible. * Creatinine ≤ 1.5 x ULN or Calculated creatinine clearance must be ≥ 50 mL/min using the Cockcroft-Gault formula. 9. Negative serum pregnancy test done ≤ 7 days prior to registration for women of childbearing potential only. NOTE: A female of childbearing potential is a sexually mature female who: * has not undergone a hysterectomy or bilateral oophorectomy; or * has not been naturally postmenopausal for at least 12 consecutive months (i.e., has had menses at any time preceding 12 consecutive months). 10. Archival tissue obtained within the previous 3 months is required if available. If interval systemic anti-cancer treatment was administered between the biopsy collection and C1D1 a new biopsy must be performed. Subjects that do not have archival tissue available (obtained within the previous 3 months, without interval systemic anti-cancer treatment) must be willing to undergo a biopsy prior to C1D1. All subjects will undergo an on-treatment biopsy at Week 6 (at the end of Cycle 2; ± 7 days) if deemed feasible and safe by the investigator. Peripheral blood samples are also required. All specimens will be used for correlative research purposes. 11. Willing to return to enrolling institution for follow-up (during the Active Monitoring Phase of the study, i.e., active treatment and safety follow-up). 12. Subject is willing and able to comply with the protocol for the duration of the study, including undergoing treatment and scheduled visits and examinations including follow-up. Exclusion Criteria: 1. History of myocardial infarction ≤ 6 months prior to registration, or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias. 2. Participation in another clinical study with an investigational product ≤ 28 days prior to registration unless it is an observational (non-interventional) clinical study or during the follow-up period of an interventional study. 3. Liver directed therapy (TACE, Y-90, liver directed radiation) ≤ 28 days prior to registration. NOTE: Prior liver directed therapy \> 28 days of registration is allowed as long as the subject has at least one measurable untreated lesion by RECIST v.1.1. 4. Any unresolved toxicity NCI CTCAE Grade ≥ 2 from previous anticancer therapy with the exception of alopecia, vitiligo, and the laboratory values defined in the inclusion criteria. * Subjects with Grade ≥ 2 neuropathy will be evaluated on a case-by-case basis after consultation with the sponsor-investigator. * Subjects with irreversible toxicity not reasonably expected to be exacerbated by treatment with durvalumab or tremelimumab may be included only after consultation with the sponsor-investigator. 5. Any concurrent chemotherapy, IP, biologic, or hormonal therapy for cancer treatment other than the study drugs. Concurrent use of hormonal therapy for non-cancer-related conditions (e.g., hormone replacement therapy) is acceptable. 6. Prior randomization or treatment in a previous durvalumab and/or tremelimumab clinical study regardless of treatment arm assignment. 7. Subjects who have received prior gemcitabine, cisplatin, anti-PD-1, anti-PD-L1 or anti-CTLA-4 for locally advanced or metastatic disease. NOTE: Prior anti-PD-1, anti-PD-L1 or anti-CTLA-4 can be allowed if it was administered for nonmetastatic and early stage disease, in that case subject: * Must not have experienced a toxicity that led to permanent discontinuation of prior immunotherapy. * All AEs while receiving prior immunotherapy must have completely resolved or resolved to baseline prior to screening for this study. * Must not have experienced a ≥ Grade 3 immune related AE or an immune related neurologic or ocular AE of any grade while receiving prior immunotherapy. NOTE: Subjects with endocrine AE of ≤ Grade 2 are permitted to enroll if they are stably maintained on appropriate replacement therapy and are asymptomatic. * Must not have required the use of additional immunosuppression other than corticosteroids for the management of an AE, not have experienced recurrence of an AE if re-challenged, and not currently require maintenance doses of \> 10 mg prednisone or equivalent per day. 8. Current or prior use of immunosuppressive medication ≤ 14 days prior to registration. The following are exceptions to this criterion: * Intranasal, inhaled, topical steroids, or local steroid injections (e.g., intra articular injection) * Systemic corticosteroids at physiologic doses not to exceed \<\<10 mg/day\>\> of prednisone or its equivalent * Steroids as premedication for hypersensitivity reactions (e.g., CT scan premedication) 9. Receipt of live attenuated vaccine ≤ 30 days prior to registration. NOTE: Subjects, if enrolled, should not receive live vaccine whilst receiving study drugs and up to 30 days after the last dose of study drugs. 10. Radiotherapy treatment to more than 30% of the bone marrow or with a wide field of radiation ≤ 28 days prior to registration. 11. Known allergy or hypersensitivity to any of the study drugs or any of the study drug excipients. 12. Major surgical procedure (as defined by the investigator) ≤ 28 days prior to registration. NOTE: Local surgery of isolated lesions for palliative intent is acceptable. 13. History of allogenic organ transplantation. 14. Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease \[e.g., colitis or Crohn's disease\], diverticulitis \[with the exception of diverticulosis\], systemic lupus erythematosus, Sarcoidosis syndrome, or Wegener syndrome \[granulomatosis with polyangiitis, Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, etc.\]). NOTE: Subjects without active disease in the last 5 years may be included but only after consultation with the study physician. The following are exceptions to this criterion. Subjects with: * Vitiligo or alopecia * Hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement * Any chronic skin condition that does not require systemic therapy * Celiac disease controlled by diet alone 15. Uncontrolled intercurrent illness, including but not limited to, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, interstitial lung disease, serious chronic gastrointestinal conditions associated with diarrhea, or psychiatric illness/social situations that would limit compliance with study requirement, substantially increase risk of incurring AEs or compromise the ability of the subject to give written informed consent. 16. History of another primary malignancy except for: * Malignancy treated with curative intent and with no known active disease ≥ 5 years prior to registration and of low potential risk for recurrence * Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease * Adequately treated carcinoma in situ without evidence of disease 17. History of leptomeningeal carcinomatosis 18. Brain metastases or spinal cord compression. NOTE: Subjects with suspected brain metastases at screening should have an MRI (preferred) or CT each preferably with IV contrast of the brain prior to study entry. Subjects that have untreated central nervous system (CNS) metastases and/or carcinomatous meningitis identified either on the baseline brain imaging obtained during the screening period or identified prior to signing the ICF are not eligible to participate. Subjects whose brain metastases have been treated may be eligible provided they show radiographic stability (defined as 2 brain scans, both of which are obtained after treatment to the brain metastases. These imaging scans should both be obtained at least four weeks apart and show no evidence of intracranial progression). In addition, any neurologic symptoms that developed either as a result of the brain metastases or their treatment must have resolved or be stable either, without the use of steroids, or are stable on a steroid dose of ≤ 10mg/day of prednisone or its equivalent and anti-convulsants ≤ 14 days prior to registration. Brain metastases will not be recorded as RECIST Target Lesions at baseline. 19. Mean QT interval corrected for heart rate using Fridericia's formula (QTcF) ≥ 470 ms calculated from 3 ECGs (within 15 minutes at 5 minutes apart). 20. History of active primary immunodeficiency. 21. Known active hepatitis infection, positive hepatitis C virus (HCV) antibody, hepatitis B virus (HBV) surface antigen (HBsAg) or HBV core antibody (anti-HBc), at screening. Subjects with a past or resolved HBV infection (defined as the presence of anti HBc and absence of HBsAg) are eligible. Subjects positive for HCV antibody are eligible only if polymerase chain reaction is negative for HCV RNA. 22. Known to have tested positive for human immunodeficiency virus (HIV) (positive HIV 1/2 antibodies). 23. Active tuberculosis infection (clinical evaluation that may include clinical history, physical examination and radiographic findings, or tuberculosis testing in line with local practice). 24. Female subjects who are pregnant or breastfeeding or male or female subjects of reproductive potential who are not willing to employ effective birth control as described in Section 5.5. NOTE: breast milk cannot be stored for future use while the subject is being treated on study.