No prior anti-MET therapy such as crizotinib or cabozantinib, or PD-1/PD-L1 immune checkpoint inhibitor therapy (such as nivolumab, pembrolizumab, atezolizumab) or CTLA4 inhibitor therapy (such as ipilimumab); no prior allergic reaction to small molecule tyrosine kinase inhibitors or monoclonal antibodies\r\n* Exception for targeted therapy sub-study (Arm T): Prior crizotinib may be allowed depending on the gene alteration Prior treatment with immune checkpoint inhibitor, including (but not limited to) those targeting PD-1, PD-L1, PD-L2, CTLA-4, CD137, GITR, TIM3, LAG3, or OX40 Prior therapy with an immune checkpoint inhibitor therapy is allowable. A 6-week washout period will be required for those with prior PD-1 or PD-L1 treatment. Subjects who have received prior anti-PD-1 or anti-PD-L1 antibody, or an IDO inhibitor; subjects who have received experimental vaccines or other immune therapies should be discussed with the principal investigator to confirm eligibility Patients who have previously received an immune checkpoint inhibitor (e.g., anti- PD-L1, anti-PD-1, anti-CTLA-4) prior to enrollment must have toxicities related to the checkpoint inhibitor resolved to ? Grade 1 or baseline (prior to the checkpoint inhibitor) to be eligible for enrollment. Patients who experienced previous hypothyroidism toxicity on a checkpoint inhibitor are eligible to enter study regardless of Grade resolution as long as the patient is well controlled on thyroid replacement hormones. Subjects who have received any prior cytotoxic therapy, immunotherapy, major surgery, antitumor vaccines or monoclonal antibodies in the 4 weeks or 5 half-lives, whichever is shorter, prior to course 1, day 1 (C1D1) (6 weeks prior for checkpoint inhibitors such as anti-CTLA-4 or anti-PD1/PD-L1 and for nitrosoureas or mitomycin C); subjects must not have received radiotherapy in the 2 weeks prior to C1D1; subjects who had grade >= 3 immune-related adverse event (irAE) during previous treatment with one of the checkpoint inhibitors are excluded from the trial; subjects who had grade 1 or 2 irAE that have resolved to grade 1 are eligible Has previously progressed on a PD-1 or PD-L1 checkpoint inhibitor for systemic disease Acceptable marrow function and hematologic indices for PD1/PDL1 immune checkpoint inhibitor and nelfinavir as per standard of care Allergy or intolerance to nelfinavir or selected PD1/PDL1 immune checkpoint inhibitor Patients should not have received prior immunotherapies (exception; arm B); they include but are not limited to interleukin-2 and other immune checkpoint antagonist targeting CTLA-4, LAG-3, TIM-3, KIR etc. and/or agonists targeting OX40, ICOS, CD137, etc\r\n* NOTE: prior cancer vaccine treatments are permitted; for arm B, exposure to single agent PD-1/PD-L1 inhibitors are allowed >= 14 days from registration Prior treatment with nivolumab or any other PD1/PDL1 checkpoint inhibitor Patients enrolled on the phase II randomized trial, who have had prior treatment with a PD1 or PDL1 inhibitor, anti-CTLA 4 antibody or any other antibody or drug that specifically targets immune checkpoint pathway (i.e. not “immune therapy naive”)\r\n* Note: for those enrolled in the phase I dose escalation, prior use of a PD1 or PDL1, anti-CTLA4 antibody or any other antibody or drug that specifically targets immune checkpoint pathway is allowed; for those enrolled in the phase IB, prior use of a PD1 or PDL1, anti-CTLA4 antibody or any other antibody or drug that specifically targets immune checkpoint pathway is required; for all patients in all phases, prior use of a vaccine for treatment of cancer is allowed Patients enrolled in the phase Ib expansion who have never previously been treated with a PD1 or PDL1 inhibitor, anti-CTLA 4 antibody or any other antibody or drug that specifically targets immune checkpoint pathway in the past (i.e. not \pre-treated”) PHASE I STUDY ELIGIBILITY CRITERIA:\r\nPatients who have had prior immune checkpoint inhibitors, such as MEDI4736 or other PD1 or PD-L1 inhibitors or an anti-CTLA4 therapy Prior treatment with immune checkpoint inhibitor, including (but not limited to) those targeting PD-1, PD-L1, PD-L2, CTLA-4, CD137, GITR, TIM3, LAG3, or OX40 TREATMENT: Patients should have been off conventional therapy for at least 1 week prior to entry in this study (except for lenalidomide, thalidomide, pomalidomide or immune checkpoint inhibitors such as CTLA4 and/or PD-1/PD-L1 inhibitors) Subjects who received prior treatment with immune checkpoint inhibition, consisting of ipilimumab, tremelimumab, nivolumab, pembrolizumab or other antibody to CTLA4 or PD-1. PD-1 / PD-L1 checkpoint inhibitor therapy is permitted; Approved PD-1/PD-L1 inhibitors, CTLA4 checkpoint inhibitors, or other immunotherapy ? 4 weeks Previous treatment with any checkpoint inhibitor such as anti-PD1 or PD-L1 agents including pembrolizumab (KEYTRUDA) or any other checkpoint inhibitor(s) (e.g., ipilimumab, nivolumab, etc.) Patients are not eligible who have received prior immunotherapy including interleukin-2 and immune checkpoint antagonists and/or agonists (including but not limited to PD-1, PD-L1, CD137, or OX40)\r\n* NOTE: Single agent anti-CTLA4 monoclonal antibody treatments are permitted; cancer vaccine therapies are permitted DOSE ESCALATION COHORT: Subjects who have received an IDO inhibitor; subjects who have received other immune checkpoint inhibitors (e.g. anti-PD-1, anti-PD-L1, and any other treatment targeting T-cell) will be permitted; subjects who have received experimental vaccines or other immune therapies should be discussed with the principal investigator (PI) to confirm eligibility DOSE EXPANSION COHORT: Subjects who have received an IDO inhibitor; subjects who have received other immune checkpoint inhibitors (e.g. anti-PD-1, anti-PD-L1, and any other treatment targeting T-cell) will be permitted; subjects who have received experimental vaccines or other immune therapies should be discussed with the PI to confirm eligibility Prior treatment-related toxicity resolved to =< grade 1 or baseline with the exception of alopecia and permanent grade =< 2 toxicities related to prior immune checkpoint inhibitor treatment (e.g. PD-1/PD-L1, CTLA-4, CD40, LAG3) treatment with the review and approval by the lead principal investigator (PI) Subject has previously been treated with a HDAC inhibitor, PD-1 inhibitor, PD-L1 inhibitor, PD-L2 inhibitor, CTLA-4 inhibitor, or any other antibody or drug specifically targeting T-cell costimulation or immune checkpoint pathways The patient may not have received treatment with immune checkpoint inhibitors (e.g., products that target PD-L1, PD-1, or CTLA-4). The patient must have received treatment with an immune checkpoint inhibitor or combination (e.g., products that target PD-1, PD-L1, or CTLA-4) or be intolerant to, or refuse such treatment. The patient may have received treatment with an immune checkpoint inhibitor (e.g., products that target PD-L1, PD-1, or CTLA-4). The patient may not have received treatment with an immune checkpoint inhibitor (e.g., products that target PD-L1, PD-1, or CTLA-4). The patient may have been treated with an immune checkpoint inhibitor (e.g., products that target PD-L1, PD-1, or CTLA-4). The patient may have been treated with an immune checkpoint inhibitor (e.g., products that target PD-L1, PD-1, or CTLA-4). The patient may not have received treatment with immune checkpoint inhibitors (e.g., products that target PD-L1, PD-1, or CTLA-4). Expansion Cohort 7: Subjects with Stage IV non-squamous NSCLC who have radiographically progressed on or after treatment with one prior immune checkpoint inhibitor (anti-PD-1 or anti-PD-L1) as the most recent therapy for metastatic disease. Expansion Cohort 8: Subjects with Stage IV non-squamous NSCLC who have not received prior immune checkpoint inhibitor therapy (anti-PD-1 or anti-PD-L1). Prior treatment with ibrutinib, a PD-1 inhibitor, a PD-L1 inhibitor, or a CTLA-4 inhibitor Has not received prior therapy with CTLA-4, PD-1/PD-L1 inhibitors, other co-stimulatory or co-inhibitory immune checkpoint antibody therapies (e.g. LAG3, TIM3, CD137, KIR3DL, CD70, and CD27) for distant metastatic melanoma; patients who have received MAPK inhibitors are allowed on condition that they have recovered from adverse events to at most grade 1 by Common Terminology Criteria for Adverse Events (CTCAE) v4.03 and at least 15 days have elapsed between last dose of MAPK inhibitors and C11-AMT imaging; patients who have previously received CTLA-4 inhibitors in the adjuvant setting are allowed to participate as long as they discontinued CTLA-4 treatment at least 30 days ago; patients who have previously received adjuvant PD- 1 inhibitors are excluded Prior treatment with PD-L1 inhibitor, PD-1 inhibitor, anti-CTLA4, anti-CD137, anti-OX40 or other immune checkpoint blockade or activator therapy with the exception of subjects who received atezolizumab in this study and are eligible for re-treatment