Combination Immunotherapy in Rare Cancers Under InvesTigation

Inclusion Criteria: 1. Signed Written Informed Consent * Subjects must be willing and able to comply with scheduled visits, treatment schedule, laboratory testing, and other requirements of the study 2. Target Population * a) Histologically confirmed Neuroendocrine cancers: Atypical bronchial carcinoid, neuroendocrine carcinoma and Grade 3 NETs independent of primary site (SCLC excluded); Biliary Tract Cancers: Intrahepatic cholangiocarcinoma, gallbladder carcinoma; Gynaecological malignancies: Ovarian clear cell carcinoma, uterine clear cell carcinoma, uterine/ovarian carcinosarcoma, uterine leiomyosarcoma, vaginal/vulva squamous cell carcinoma; Mismatch repair protein deficient (MSI-H) cancers (excluding colorectal carcinoma) * Eastern Cooperative Oncology Group (ECOG) performance status of ≤1 * Prior systemic therapy (≤1) for advanced disease is permitted if it was completed at least 4 weeks prior to enrolment, and all related adverse events have either returned to baseline or stabilized or participants are not suitable for, or if declining established standard therapies. For MSI-H rare cancers and atypical bronchial carcinoid only, patients will be eligible independent of the number of prior lines of systemic treatment received as long as treatment has been completed at least 4 weeks prior to enrolment. * Prior radiotherapy must have been completed at least 2 weeks prior to study drug administration. * Measurable disease by CT or MRI per RECIST 1.1 criteria * Tumour tissue from an unresectable or metastatic site of disease must be available for biomarker analyses. * Screening laboratory values must meet the following criteria and should be obtained within 14 days prior to randomization: * WBC (white blood cells) \> or = to 2000/μL * Neutrophils \> or = to 1500/μL * Platelets \> or = to 100 x103/μL * Hemoglobin \> 9.0 g/dL * Serum creatinine \< or = to 1.5 x ULN or creatinine clearance (CrCl) 40 mL/min (using the Cockcroft-Gault formula) * AST/ALT (aspartate transaminase/alanine transaminase) \< or = to 3 x ULN (in the event of metastatic liver disease, an exception to this upper limit may be accepted in consultation with the study physician). * Total Bilirubin \< or = to 1.5 x ULN (Upper limit of normal) (except subjects with Gilbert Syndrome, who can have total bilirubin \< 3.0 mg/dL). * Subject Re-enrolment: This study permits the re-enrolment of a subject that has discontinued the study as a pre-treatment failure (i.e. subject has not been treated) after obtaining agreement from the medical monitor prior to re enrolling a subject. If re-enrolled, the subject must be re-consented. 3. Age and Reproductive Status * Men and women, \> or = to 18 years of age * Women of childbearing potential (WOCBP) must use method(s) of contraception. WOCBP should therefore use an adequate method to avoid pregnancy for 23 weeks (30 days plus the time required for Nivolumab to undergo five half lives) after the last dose of investigational drug. * Women must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 24 hours prior to the start of investigational product. * Women must not be breastfeeding * Men who are sexually active with WOCBP must use any contraceptive method with a failure rate of less than 1 percent per year. Men that are sexually active with WOCBP must follow instructions for birth control when the half life of the investigational drug is greater than 24 hours, contraception should be continued for a period of 90 days plus the time required for the investigational drug to undergo five half lives. The half life of nivolumab and ipilimumab is up to 25 days and 18 days, respectively. Given the blinded nature of the study, men who are sexually active with WOCBP must continue contraception for 31 weeks (90 days plus the time required for nivolumab to undergo five half lives) after the last dose of investigational drug. * Women who are not of childbearing potential (i.e. who are postmenopausal or surgically sterile and azoospermic men do not require contraception. Exclusion Criteria: 1. Target Disease Exceptions * Active brain metastases or leptomeningeal metastases. Subjects with brain metastases are eligible if these have been treated and there is no magnetic resonance imaging (MRI except where contraindicated in which CT scan is acceptable) evidence of progression for at least 8 weeks after treatment is complete and within 28 days prior to first dose of study drug administration. Cases should be discussed with the medical monitor. There must also be no requirement for immunosuppressive doses of systemic corticosteroids (\> 10 mg/day prednisone equivalents) for at least 2 weeks prior to study drug administration. 2. Medical History and Concurrent Diseases * Prior combination treatment directed against the PD-1/PDL1 (Programmed Death Ligand 1) axis (anti PD 1, anti PD-L1, anti PD L2), and anti CTLA 4 antibody. Prior monotherapy with these agents or other immune-stimulating/regulating agents is permitted. * Any serious or uncontrolled medical disorder that, in the opinion of the investigator, may increase the risk associated with study participation or study drug administration, impair the ability of the subject to receive protocol therapy, or interfere with the interpretation of study results. * 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. * Subjects with active, known or suspected autoimmune disease. Subjects with vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll. * Subjects with a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration. Inhaled or topical steroids, and adrenal replacement doses \> 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. 3. Physical and Laboratory Test Findings * Any positive test result for hepatitis B virus or hepatitis C virus indicating acute or chronic infection * Known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS). 4. Allergies and Adverse Drug Reaction * History of allergy to study drug components. * History of severe hypersensitivity reaction to any monoclonal antibody. 5. Sex and Reproductive Status * WOCBP who are pregnant or breastfeeding * Women with a positive pregnancy test at enrolment or prior to administration of study medication. 6. Other Exclusion Criteria * Prisoners or subjects who are involuntarily incarcerated * Subjects who are compulsorily detained for treatment of either a psychiatric or physical (e.g. infectious disease) illness.