Study of Combination Therapy With the MEK Inhibitor, Cobimetinib, Immune Checkpoint Blockade, Atezolizumab, and the AUTOphagy Inhibitor, Hydroxychloroquine in KRAS-mutated Advanced Malignancies

Inclusion Criteria: 1. Histological or pathological confirmation of malignancy with a KRAS-activating mutation. 2. Extent of disease Advanced disease for which no curable options are available. Subjects who are not deemed candidates for these curative therapies will be eligible if they meet other criteria. 3. Prior treatments * Pancreatic adenocarcinoma Subjects must have progressed on or be intolerant of combination therapy containing either 5-Fluorouracil/Capecitabine- and/or gemcitabine-based therapy. Subjects who experienced disease recurrence while receiving adjuvant chemotherapy or within three months of completing adjuvant chemotherapy are eligible. * Colorectal adenocarcinoma Subjects must have progressed on or be intolerant of combination therapy containing 5-Fluorouracil/Capecitabine, and must have received Oxaliplatin and Irinotecan. * MSI-H/dMMR or NTRK-fusion positive tumors Subjects must have received prior treatment with approved drugs for tumors harboring these aberrations. * Histology agnostic cancers other than pancreatic and colorectal adenocarcinoma (see above; Phase 1 and 2) Subjects must have progressed on or be intolerant of all standard of care therapies that result in a median progression free survival benefit of ≥ 8 weeks, or overall response rate of \>5%. 4. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 5. Age ≥18 years 6. Adequate hematological and end-organ function (test results from within 14 days prior to initiation of study treatment): * Absolute neutrophil count (ANC) ≥ 1.5 x 109/L without granulocyte colony-stimulating factor support * White blood cell (WBC) count ≥ 2.5 x 109/L * Lymphocyte count ≥ 0.5 x 109/L * Platelet count ≥ 100 x 109/L without transfusion * Hemoglobin (Hgb) \> 9.0 g/dL * Aspartate aminotransferase (AST), alanine aminotransferase (ALT), and alkaline phosphatase (ALP) ≤ 2.5 x upper limit of normal (ULN), unless elevated secondary to bilary obstruction from the pancreas mass and amenable to decompression prior to initiation of therapy * Serum total bilirubin ≤ 1.5 x ULN, unless in patients with known Gilbert disease (≤ 3 x ULN), or unless elevated secondary to bilary obstruction from the pancreas mass and amenable to decompression prior to administration of investigational therapy * Albumin ≥ 3.0g/dL * Creatinine within ULN or calculated creatinine clearance (CrCl) \>50 mL/min using the Cockcroft-Gault formula * International Normalized Ratio (INR) and activated partial thromboplastin time (aPTT) ≤ 1.5 x ULN except for those who are on stable anticoagulation for at least three months. 7. Measurable disease according to Immune-modified Response Evaluation Criteria in Solid Tumors (IM-RECIST) and tumor accessible for fresh biopsy if ten adequate paired biopsied specimens have not been procured (Phase 1) 8. Negative pregnancy test and agree to effective form of contraception. 9. Birth control agreement Fertile men must agree to use an effective method of birth control during the study and for up to 3 months after the last dose of study drug. 10. Informed consent Participants must be willing and able to provide written informed consent prior to any study-related procedures and to comply with all study requirements. 11. Ability to comply Participants must be able to comply with the study protocol, according to the investigator's judgement. 12. Deep venous thrombosis (DVT) testing Participants must have undergone lower extremity dopplers to rule out DVT within the screening period, and undergo therapeutic anticoagulation if evidence of DVT is identified. 13. Venous thromboembolism (VTE) testing Patients deemed at increased risk of VTE based on primary cancer, which includes pancreatic adenocarcinoma, gastric/gastroesophageal junction adenocarcinoma, or central nervous system (CNS) malignancy, are to undergo prophylaxis anticoagulation with enoxaparin. Subjects who are unable to receive enoxaparin ,but deemed at increased risk of VTE will not be eligible and consultation with the Principal Investigator is required. 14. Anticoagulation treatment Subjects who are stable on full-dose anticoagulation medication for at least 8 weeks are considered eligible. However, subjects who have an increased clot burden on full-dose anticoagulation will be considered eligible only with the approval of the Principal Investigator. Exclusion Criteria: 1. Prior treatment with investigational therapy. Participants may not have had any treatments with investigational therapy within the 28 days prior to initiation of study treatment. 2. Prior radiation therapy Participants may not have had radiation therapy within 2 weeks prior to initiation of study treatment. Participants may not have had previous radiotherapy to 25% or more of the bone marrow. 3. Prior Therapy Participants may not have had systemic chemotherapy within 14 days or 5 half-lives of the drug (whichever is longer) prior to initiation of study treatment. In addition, the following prior treatment is not allowed during Phase 1 of the study: * Receptor tyrosine kinase inhibitors targeting MAP kinase pathway; * Any pharmacological agents inhibiting the autophagy pathway. In addition, the following prior treatment is not allowed during Phase 2 of the study: * T-cell co-stimulating agents or immune checkpoint blockade therapies * Receptor tyrosine kinase inhibitors targeting Mitogen-Activated Protein (MAP) kinase pathway; * Any pharmacological agents inhibiting the autophagy pathway. 4. Adverse events from prior anti-cancer therapy Participants may not initiate treatment if they have adverse events from prior anti-cancer therapy that have not resolved to Grade ≤ 1 or better, with the exception of Grade ≤ 2 peripheral neuropathy or any grade alopecia. 5. Patients currently receiving any other investigational agents 6. Concomitant treatment with other anti-neoplastic agents (hormone therapy acceptable) 7. Uncontrolled pleural effusion, pericardial effusion, or ascites 8. Patients with symptomatic brain metastases Subjects with untreated brain metastasis ≤ 1 cm can be considered eligible if deemed asymptomatic by the investigator upon consultation with the medical monitor, and do not require immediate radiation or steroids. Subjects with brain metastasis that is treated and stable for 1 month may be considered eligible if they are asymptomatic and on stable dose of steroids, or if they do not require steroids following successful local therapy. 9. Uncontrolled hypercalcemia or symptomatic hypercalcemia requiring continued use of bisphosphonate therapy. 10. Recent major surgery or significant traumatic injury Participants may not have undergone major surgery or experienced significant traumatic injury within 14 days prior to initiating study treatment, or be recovering from a procedure related to adverse events of ≤ Grade 1. 11. Active or history of autoimmune disease or immune deficiency With the following exceptions: * Patients with a history of autoimmune-related hypothyroidism who are on stable thyroid-replacement hormone are eligible for the study. * Patients with controlled Type 1 diabetes mellitus who are on a stable insulin regimen are eligible for the study. * Patients with eczema, psoriasis, lichen simplex chronicus, or vitiligo with dermatologic manifestations only are eligible for the study provided all of following conditions are met: * Rash must cover \<10% of body surface area; * Disease is well-controlled at baseline and requires only low-potency topical corticosteroids; * No occurrence of acute exacerbations of the underlying condition requiring psoralen plus ultraviolet A radiation, methotrexate, retinoids, biologic agents, oral calcineurin inhibitors, or high-potency or oral corticosteroids within the previous 12 months. 12. History of idiopathic pulmonary fibrosis, interstitial lung disease, organizing pneumonia, drug-induced pneumonitis, or idiopathic pneumonitis, or evidence of active pneumonitis on screening chest computed tomography scan \[history of radiation pneumonitis in the radiation field (fibrosis) is permitted\]. 13. Positive for HIV at screening or any time prior to screening Patients without prior positive HIV test result will undergo an HIV test at screening, unless not permitted under local regulations. 14. Active Hepatitis B virus (HBV) infection (chronic or acute) Defined as having a positive hepatitis B surface antigen (HBsAg) test at screening. Patients with a past or resolved HBV infection, defined as having a negative HBsAg test and a positive total hepatitis B core antibody test at screening, are eligible for the study. 15. Active hepatitis C virus (HCV) infection Defined as positive HCV antibody test followed by a positive HCV RNA test at screening. The HCV RNA test will be performed only for patients who have a positive HCV antibody test. 16. Known clinically significant liver disease 17. Active tuberculosis 18. Severe infection Patients may not have had a severe infection within 4 weeks prior to initiation of study treatment. This includes, but is not limited to, hospitalization for complications of infection, bacteremia, or severe pneumonia. However, patients who were admitted for biliary tract infection due to bile duct obstruction at time of diagnosis must have a functioning biliary stent (as evidenced by declining total bilirubin and ≤ 2 x ULN) and resolved infection (defined by normalization of elevated white blood cell count, absence of signs of infection) and completion of an antibiotic course (at least a seven-day course) prior to initiation of therapy. 19. Recent antibiotic treatment Patients may not have been treated with therapeutic oral or intravenous (IV) antibiotics within 2 weeks prior to initiation of study treatment, except for biliary tract infection due to bile duct obstruction from the pancreas mass. Patients receiving prophylactic antibiotics are eligible for the study. 20. Significant cardiovascular disease Patient may not have significant cardiovascular disease within 12 months prior to initiation of study treatment, seizure disorder, uncontrolled hypertension, or unstable arrhythmia or unstable angina within 3 months prior to initiation of study treatment. 21. Left ventricular ejection fraction below institutional lower limit of normal or below 50%, whichever is lower 22. Baseline QTcF ≥ 450 ms (males) or ≥ 470 ms (females) 23. Grade ≥ 3 hemorrhage or bleeding event within 28 days prior to initiation of study treatment 24. Prior autologous stem cell, allogeneic stem cell, or solid organ transplantation 25. History of malignancy Patient may not have a history of malignancy other than PDA within 2 years prior to screening, with the exception of those with a negligible risk of metastasis or death. 26. Recent vaccination Patients may not have been treated with a live, attenuated vaccine within 4 weeks prior to initiation of study treatment, or anticipate the need for such a vaccine during treatment with atezolizumab or within 5 months after the last dose of atezolizumab. 27. History of severe allergic anaphylactic reactions to chimeric or humanized antibodies or fusion proteins 28. Known allergy or hypersensitivity to 4-aminoquinoline compounds or any of the study drug excipients 29. Recent immunosuppressive treatment Patients may not have been treated with systemic immunosuppressive medication within 2 weeks prior to initiation of study treatment, or anticipate the need for systemic immunosuppressive medication during the course of the study, with the following exceptions: * Patients who received mineralocorticoids, corticosteroids for chronic obstructive pulmonary disease or asthma, or low-dose corticosteroids for orthostatic hypotension or adrenal insufficiency are eligible for the study if receiving equivalent to \< 10mg of prednisone daily. * Patients who received a one-time pulse dose of systemic immunosuppressant medication are eligible for the study after approval from the Principal Investigator. 30. Inability to swallow medication or malabsorption condition that would alter the absorption of orally administered medications 31. History of retinal pathology Specifically, patients will be excluded from study participation if they currently are known to have any risk factors for retinal vein occlusion (RVO), including: * Glaucoma with intraocular pressure ≥ 21 mmHg; * Grade ≥ 2 serum cholesterol; * Grade ≥ 2 hypertriglyceridemia; * Grade ≥ 2 uncontrolled hypertension (patients with a history of hypertension controlled with anti-hypertensive medication to Grade ≤ 1 are eligible). 32. Pregnancy and breastfeeding 33. Other contraindicated conditions (opinion of treating investigator) 34. Concomitant strong CYP3A4 inhibitors and inducers Concomitant treatment is permitted if the medication is not expected to interfere with the evaluation of safety or efficacy of the study drug. 35. Uncontrolled psoriasis, porphyria, proximal myopathy or neuropathy 36. Severe depression Subjects hospitalized for depression within the past 2 years, or who have prior suicidal attempts will be excluded. 37. Glucose-6-phosphate dehydrogenase deficiency 38. History of connective tissue disorders 39. Subjects on greater than once daily dose of antacid therapy 40. Concomitant use of any of the following drugs: * Digoxin * Pharmacological agents known to prolong QT interval * Mefloquine or other agents which may lower the convulsive threshold * Antiepileptics * Methotrexate * Cyclosporine * Ampicillin * Cimetidine