Study of ARRY-614 Plus Either Nivolumab or Nivolumab+Ipilimumab

Inclusion Criteria: * Age ≥18 years. * For Phase Ib: Trial participants must have a histologically confirmed malignancy that is metastatic or unresectable for which curative measures do not exist or are no longer effective. a.Trial participants must have nivolumab or ipilimumab therapy available and must be appropriate for this therapy. * For Phase II: 1. Participants with melanoma who previously experienced disease progression on anti-PD1 (with or without ipilimumab). 2. Participants with RCC who previously experienced disease progression on anti-PD1 (with or without ipilimumab). 3. Participants with NSCLC or HNSCC who previously experienced disease progression on anti-PD1 (with or without ipilimumab). 4. Progression on prior anti-PD1/L1 or anti-PD1/anti-CTLA4 antibodies must meet definitions for primary or secondary resistance and regrowth after stopping therapy as below or there must be documentation by the treating investigator of rapid disease progression such that these criteria cannot be assessed (suggestions from the Society for ImmunoTherapy of Cancer PD1 Resistance Working Group). * Have an ECOG PS score of 0 or 1 (Appendix 13.A). * Have an expected survival of ≥3 months. * Have at least one evaluable and measurable lesion as defined by RECIST v1.1. * The first five patients in each Phase II cohort must have tumors determined to be easily accessible for biopsy and must be willing to have two biopsies * Have recovered from toxicities associated with prior anticancer therapy to baseline or Grade 1 unless stabilized under medical management per investigator. * Have adequate bone marrow function as evidenced by: 1. Absolute neutrophil count ≥1,500/mm3 or 1.5 ×109/L 2. Hemoglobin ≥8 g/dL 3. Platelets ≥100,000/mm3 or 100 × 109/L * Have adequate hepatic function as evidenced by: 1. Serum total bilirubin ≤2 × upper limit of normal (ULN), unless considered due to Gilbert's disease 2. Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5x the institutional ULN or ≤ 5.0x institutional ULN in the presence of known liver metastases. * Patients with creatinine clearance \> 30 mL/min, (measured using Cockcroft-Gault equation or the estimated glomerular filtration rate from the Modification of Diet in Renal Disease Study) are included in the study. * Be able to understand and willing to sign the informed consent form (or have legal representation) and to comply with scheduled visits, treatment plans, procedures, and laboratory tests, including serial peripheral blood sampling, biopsies, and urine sampling, during the study. A legally authorized representative may consent on behalf of a subject who is otherwise unable to provide informed consent if acceptable to and approved by the site's IRB/Independent Ethics Committee (IEC). * Female patients with reproductive potential must have a negative serum pregnancy test prior to the start of therapy, or a confirmation from an obstetrician in case of equivocal serum pregnancy results. Females of reproductive potential are defined as sexually mature women who have not undergone a hysterectomy, bilateral oophorectomy, or tubal occlusion or who have not been naturally postmenopausal (ie, who have not menstruated) for at least 24 consecutive months (ie, have not had menses at any time in the preceding 24 consecutive months). Women with reproductive potential, as well as fertile men and their partners who are female with reproductive potential, must agree to use two effective forms of contraception (including at least one barrier form) from the time of giving informed consent throughout the study and for 5 months after the last dose of therapy for women, and 7 months after last dose for men. Effective forms of contraception are defined as hormonal PO contraceptives, injectables, patches, intrauterine devices, intrauterine hormone-releasing systems, bilateral tubal ligation, condoms with spermicide, or male partner sterilization. * Patients positive for human immunodeficiency virus (HIV) are NOT excluded from this study, but HIV-positive patients must have: 1. A stable regimen of highly active anti-retroviral therapy (HAART) 2. No requirement for concurrent antibiotics or antifungal agents for the prevention of opportunistic infections 3. A CD4 count above 250 cells/mcL and an undetectable HIV viral load on standard PCR-based test Exclusion Criteria: * Received systemic anticancer therapy or an investigational agent \<2 weeks prior to Day 1 (washout from prior immune based anticancer therapy is 4 weeks). In addition, the first dose of study treatment should not occur before a period ≥5 half-lives of the investigational agent has elapsed (excluding nivolumab therapy or combination anti-PD1/ipilimumab combination therapy in RCC - prior ipilimumab not permitted in melanoma cohort). * For ST, have underwent hepatic radiation, chemoembolization, and radiofrequency ablation \<4 weeks prior to Day 1. * Participants must not have had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study Day 1 (with exception of anti-PD1/ipilimumab combination therapy) or have not recovered (i.e. \< Grade 1 at baseline) from adverse events due to agents administered more than 4 weeks earlier. * Participants must not have a diagnosis of immunodeficiency or be receiving systemic steroid therapy at a dose of \>10 mg prednisone daily or equivalent at time of first dose of trial treatment (this criterion does not apply to HIV-positive patients as detailed in the inclusion criteria). * Participants must not have active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g. thyroxine, insulin, or physiologic corticosteroids replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. * Participants must not have a known history of non-infectious pneumonitis that required steroids for treatment. * Participants must not have evidence of active interstitial lung disease. * Have known symptomatic brain metastases requiring steroids. Patients with previously diagnosed brain metastases are eligible if they have completed their treatment and have recovered from the acute effects of radiation therapy or surgery prior to study entry, have discontinued corticosteroid treatment for these metastases for at least 1 week and have radiographically stable disease for at least 1 month prior to study entry. Note: up to 10 mg per day of prednisone equivalent will be allowed. * Have a history of another primary cancer that is active requiring treatment, progressing or for which the investigator believes will make disease assessment unreliable. * Underwent major surgery within 4 weeks of Day 1 or have not recovered from post-surgery toxicities. * Are pregnant or breastfeeding. * Have an active infection requiring systemic anti-infective therapy or with an unexplained fever \>38.5°C within 7 days of Day 1 (at the discretion of the Investigator, patients with tumor fever may be enrolled). * Have any known hypersensitivity to any of the components of ARRY-614 or anti-PD1/ipilimumab combination therapies. * Have significant active cardiac disease within 6 months prior to the start of study treatment, including New York Heart Association (NYHA) Class III or IV congestive heart failure); myocardial infarction; unstable angina; and/or stroke. * Have known LVEF \<40% by ECHO scan (or by other methods according to institutional practice) obtained within 28 days prior to the start of study treatment (testing is not otherwise mandatory). * Have known active hepatitis B (HBV) or hepatitis C (HCV) infections. Patients with a sustained viral response to HCV treatment or immunity to prior HBV infection will be permitted. Patients with chronic HBV that is adequately suppressed per institutional practice will be permitted. * Have any other acute or chronic medical or psychiatric condition, including recent (within 12 months of Day 1) or active suicidal ideation or behavior, or a laboratory abnormality that may increase the risk associated with study participation or investigational product administration or may interfere with the interpretation of study results and, in the judgment of the Investigator, would make the subject inappropriate for entry into this study. * Have known active inflammatory gastrointestinal disease, chronic diarrhea, previous gastric resection or lap band dysphagia, short-gut syndrome, gastroparesis, or other conditions that limit the ingestion or gastrointestinal absorption of drugs administered PO. Gastroesophageal reflux disease under medical treatment is allowed (assuming no drug interaction potential). * Have been committed to an institution by an order issued either by the judicial or administrative authorities.