Durvalumab With or Without Tremelimumab in Advanced Incurable Solid Malignancies Given With or Without Standard Chemotherapy Regimens

Inclusion Criteria: * Patients must have histologically and/or cytologically confirmed cancer that is advanced / metastatic / recurrent or unresectable and for which no curative therapy exists. * Patients must be considered suitable candidates for and eligible to receive one of the regimens (including durvalumab and tremelimumab alone (dose level 5) included in this protocol and which is open to accrual. For each regimen, specific criteria for registration may be applicable to the cohort/dose level to ensure tolerability in the planned phase II or III trials. Centres must confirm that the planned cohort is open to accrual and whether there are any restrictions on tumour types prior to approaching patients. * For etoposide/carboplatin regimen, patients must have untreated small cell lung cancer (SCLC). * If a formalin fixed paraffin embedded tissue block (from their primary or metastatic tumour) is available, patients must have provided informed consent for the release of the block. All patients must have provided informed consent for correlative studies. * Presence of clinically and/or radiologically documented disease. All radiology studies must be performed within 28 days prior to registration (within 35 days if negative). Patients ideally should have measurable disease. * Patients must have an ECOG performance status of 0, 1, or 2 (0 or 1 for untreated SCLC enrolled to etoposide/carboplatin). Patients with PS 2 must be considered fit for first line cytotoxic or immune based therapy and discussed with CCTG prior to enrolment. Previous Therapy • Cytotoxic Chemotherapy: All Cohorts Except Etoposide-Carboplatin: • Patients should not have received prior chemotherapy for advanced disease. Exceptions may be made for selected patients and regimens. Patients planned for dose level 5 may have received one line or prior chemotherapy. Consult CCTG before approaching patients. Notes: Patients planned for cisplatin regimens should have received no more than 250mg mg/m2 prior to cisplatin. Etoposide-Carboplatin Cohort: • For dose levels 0-3, patients with untreated SCLC must have received two cycles of their first etoposide carboplatin regimen prior to registration to that chemotherapy cohort. For dose level 4, SCLC patients planned for the etoposide/carboplatin cohort may not have had prior chemotherapy regimens and do not have to have their first two cycles of etoposide-platinum prior to study entry. Other Systemic Therapy: * Patients may have received other prior therapies including immunotherapy, angiogenesis inhibitors, PARP inhibitors or signal transduction inhibitors. Patients who have received other treatment with PD-L1 / PD-1, CTLA4 or other antibodies must not have had intolerable toxicity or required steroids to manage toxicity. * Patients must have recovered from all reversible toxicity related to prior chemotherapy or systemic therapy and have adequate washout as follows: Longest of one of the following: * Two weeks * 5 half lives for investigational agents * Standard cycle length of standard therapies Radiation: • Prior external beam radiation is permitted provided a minimum of 28 days (4 weeks) have elapsed between the last dose of radiation and date of registration. Exceptions may be made for low-dose, non-myelosuppressive radiotherapy after consultation with CCTG. Concurrent radiotherapy is not permitted. Patients planned for concurrent chemotherapy-radiation are not eligible. Patients with curative doses of radiation to marrow-bearing areas may not be eligible. Consult CCTG. Surgery: • Previous surgery is permitted provided that a minimum of 28 days (4 weeks) have elapsed between any major surgery and date of registration, and that wound healing has occurred. * Patients must have recovered from any treatment related toxicities prior to registration (unless grade 1, irreversible, or considered by investigator as not clinically significant). * Hematology: Absolute neutrophils ≥ 1.5 x 10\^9/L Platelets ≥ 100 x 10\^9/L Hemoglobin ≥ 90 g/L * Chemistry: Bilirubin ≤ 1.5 x ULN (upper limit of normal) \* If confirmed Gilbert's, eligible providing ≤ 3 x UNL; AST and ALT ≤ 2.5 x ULN (if liver metastases are present, ≤5 x UNL) Serum creatinine \< 1.25 x ULN or: Creatinine clearance ≥ 50 mL/min * Patient consent must be appropriately obtained in accordance with applicable local and regulatory requirements. Each patient must sign a consent form prior to registration in the trial and prior to tests which are considered to be study specific to document their willingness to participate. Patients who cannot give informed consent (i.e. mentally incompetent patients, or those physically incapacitated such as comatose patients) are not to be recruited into the study. Patients competent but physically unable to sign the consent form may have the document signed by their nearest relative or legal guardian. Each patient will be provided with a full explanation of the study before consent is requested. * Female patients of childbearing potential who are sexually active with a non sterilized male partner must use at least one highly effective method of contraception while on study and for 6 months after the last dose of durvalumab and tremelimumab or for 3 months after the last dose of durvalumab alone and consult product monograph for standard chemotherapy. Male partners of a female subject and non-sterilized male patients who are sexually active with a female partner of childbearing potential must use male condom plus spermicide while on study and for 6 months after the last dose of durvalumab and tremelimumab or for 3 months after the last dose of durvalumab alone and consult product monograph for standard chemotherapy. Female partners of a male subject must use a highly effective method of contraception throughout this period. Cessation of birth control after this point should be discussed with a responsible physician. * Male patients should also refrain from donating sperm. * Patients must be accessible for treatment and follow up. Patients registered on this trial must be treated and followed at the participating centre. This implies there must be reasonable geographical limits (for example: 1 ½ hour's driving distance) placed on patients being considered for this trial. Investigators must assure themselves the patients registered on this trial will be available for complete documentation of the treatment, response assessment, adverse events, and follow-up. * In accordance with CCTG policy, protocol treatment is to begin within 2 working days of patient registration Exclusion Criteria: * Patients with a history of other malignancies requiring concurrent anticancer therapy. * 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, celiac disease or other serious gastrointestinal chronic conditions associated with diarrhea), systemic lupus erythematosus, Sarcoidosis syndrome, or Wegener syndrome (granulomatosis with polyangiitis), rheumatoid arthritis, hypophysitis, uveitis, etc., within the past 3 years prior to the start of treatment. The following are exceptions to this criterion: * Patients with alopecia. * Patients with Grave's disease, vitiligo or psoriasis not requiring systemic treatment (within the last 2 years). * Patients with hypothyroidism (e.g. following Hashimoto syndrome) stable on hormone replacement. * History of primary immunodeficiency, history of allogenic organ transplant that requires therapeutic immunosuppression and the use of immunosuppressive agents within 28 days of registration\* or a prior history of severe (grade 3 or 4) immune mediated toxicity from other immune therapy or grade ≥ 3 infusion reaction. \* NOTE: Intranasal/inhaled corticosteroids or systemic steroids that do not to exceed 10 mg/day of prednisone or equivalent dose of an alternative corticosteroid are permissible. * Live attenuated vaccination administered within 30 days prior to registration. * History of hypersensitivity to durvalumab or tremelimumab or any excipient. Patients who have received other treatment with PD-L1 / PD-1, CTLA4 or other antibodies must not have had intolerable toxicity or required steroids to manage toxicity. * Mean QT interval corrected for heart rate using Fridericia's formula (QTcF) ≥ 470 msec in screening ECG measured using standard institutional method or history of familial long QT syndrome. * Patients who have experienced untreated and/or uncontrolled cardiovascular conditions and/or have symptomatic cardiac dysfunction (unstable angina, congestive heart failure, myocardial infarction within the previous year or cardiac ventricular arrhythmias requiring medication, history of 2nd or 3rd degree atrioventricular conduction defects). Patients with a significant cardiac history, even if controlled, should have a LVEF ≥ 50%. * Concurrent treatment with other investigational drugs or anti-cancer therapy. * Patients with serious illnesses or medical conditions which would not permit the patient to be managed according to the protocol. This includes but is not limited to: * history of significant neurologic or psychiatric disorder which would impair the ability to obtain consent or limit compliance with study requirements; * active infection requiring systemic therapy; (including any patient known to have active hepatitis B, hepatitis C or human immunodeficiency virus (HIV) or tuberculosis or any infection requiring systemic therapy); * active peptic ulcer disease or gastritis; * untreated symptomatic brain metastases or brain metastases in whom radiation or surgery is indicated. * pneumonitis * Pregnant or lactating women. Women of childbearing potential must have a urine pregnancy test (urine or serum) proven negative within 14 days prior to registration. Men and women of child-bearing potential must agree to use adequate contraception. * Not able to receive the standard chemotherapy regimen (consult product monograph).