Inclusion Criteria:  Participants must have signed and dated an Institutional Review Board (IRB)/International Electrotechnical Commission (IEC) approved written informed consent form in accordance with regulatory and institutional guidelines. This must be obtained before the performance of any protocol related procedures that are not part of normal participant care Participants must be willing and able to comply with scheduled visits, treatment schedule, laboratory testing, tumor biopsies, and other requirements of the study All consented participants should be registered in the institutional database CORe COHORT 1: Histologically confirmed stage III (unresectable) or stage IV melanoma, as per American Joint Committee on Cancer (AJCC) version 8 staging system. Patients must consent to BRAF testing or have documented BRAF status as per regionally acceptable V600 mutational status testing. Twenty biopsiable patients will be enrolled. Specifically, 25 melanoma will be enrolled in expansion cohort. 20 biopsiable will include pts in expansion cohorts COHORT 1: Have not received prior anti-cancer therapy for advanced or metastatic melanoma COHORT 1: Treatment-naïve participants (i.e., no prior systemic anticancer therapy for unresectable or metastatic melanoma) with the exception of prior adjuvant treatment for melanoma with approved agents (eg, BRAF/MEK inhibitors, ipilimumab, nivolumab, pembrolizumab or interferon). Participants who have had recurrence within the 6 months of completing adjuvant treatment are not eligible COHORT 2: Histologically or cytologically documented locally advanced or transitional cell carcinoma of the urothelium including renal pelvis, ureters, urinary bladder, or urethra. Patients with mixed histologies are required to have a dominant transitional cell pattern COHORT 2: Enrollment of urothelial carcinoma 1st line patients who are cisplatin-ineligible and who, after consultation with the investigator, choose to forego front-line chemotherapy or immunotherapy  COHORT 2: Treatment naive, cisplatin-eligible patients who refuse chemotherapy standard of care or treatment naive, cisplatin-ineligible patients who meet at least one of the following criteria:  Common Terminology Criteria for Adverse Events (CTCAE) version (v)5 grade >= 2 audiometric hearing loss. CTCAE v5 grade >= 2 peripheral neuropathy. Cisplatin ineligibility defined as: Glomerular filtration rate (GFR) less than 60 and >= 15 mL/min or; chronic heart failure (CHF) New York Heart Association (NYHA) class III or higher or; peripheral neuropathy grade 2 or higher or Eastern Cooperative Oncology Group (ECOG) performance status (PS) 2 or higher or; impaired hearing grade 2 or higher. GFR is either measured using a 24 hour urine, calculated using Cockcroft-Gault, or estimated using the Modification of Diet in Renal Disease (MDRD) method from the National Kidney Disease Education Program (NKDEP) (the method reported by MD Anderson Cancer Center [MDACC] laboratories) COHORT 2: No prior chemotherapy for inoperable locally advanced or metastatic urothelial carcinoma COHORT 2: Prior local intravesical chemotherapy is allowed if completed at least 4 weeks prior to the initiation of study treatment COHORT 2: For patients who received prior adjuvant/neoadjuvant chemotherapy or chemo-radiation for urothelial carcinoma, a treatment-free interval of more than 12 months between the last treatment administration and the date of recurrence is required to be considered treatment naive in the metastatic setting. Patients must not have received neoadjuvant or adjuvant therapy with any immuno-oncology regimens. Please note that this small population of patients will be excluded  COHORT 3: Subjects diagnosed with histologically or cytologically confirmed locally advanced/metastatic NSCLC with EGFR mutation known to be associated with EGFR tyrosine kinase inhibitor (TKI) sensitivity (including G719X, exon 19 deletion, L858R, L861Q).  Subjects must have received one prior line of therapy with an EGFR TKI in the locally advanced/metastatic setting COHORT 3: Subjects need to meet either A or B. A) Must have received and progressed on an approved first or second generation EGFR TKI (eg, erlotinib or gefitinib [first generation] or afatinib [second generation]) and must be T790M negative by an approved testing assay on tumor biopsy at the time of progression. B) Patient must have received third generation TKI Osimertinib and progressed on this therapy for study entry. C) TKI needs to be the last therapy. D) Prior chemotherapy received in the neoadjuvant or adjuvant settings will not be considered a line of therapy Participants must have an Eastern Cooperative Oncology Group (ECOG) performance status of =< 1 (adults 18 years or older) Measurable disease by computed tomography (CT) or magnetic resonance imaging (MRI) per RECIST 1.1 criteria Participants with stable brain metastases =< 3 cm, with no clinical requirement for local intervention (surgery, radiosurgery, corticosteroid therapy) or other systemic therapy are allowed to enroll. Subjects must be free of neurologic signs and symptoms related to metastatic intracranial lesions and must not have required or received systemic corticosteroid therapy within 10 days prior to first treatment All participants must have tissue submitted during screening. Either a formalin-fixed, paraffin-embedded (FFPE) tissue block or unstained tumor tissue sections, obtained within 3 months prior to enrollment. Biopsy should be excisional, incisional, punch biopsy, core needle or surgical specimen. Fine needle aspiration is unacceptable for submission. Biopsies of bone lesions that do not have a soft tissue component are also unacceptable for submission Prior palliative radiotherapy must be completed at least 2 weeks prior to day 1 of study treatment. Participants must have recovered from all radiation-related toxicities. Note: radiated lesions cannot be used as measurable lesions unless there is clear evidence of progression Participants must be able and willing to comply with the study visit schedule and study procedures A documented left ventricular ejection fraction (LVEF) > 45% using standard echocardiogram or multigated acquisition (MUGA) scan test within 60 days prior to study treatment initiation Males and females, ages 18 years or older Women of childbearing potential (WOCBP) must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin [HCG]) within 24 hours prior to the start of study treatment Women must not be breastfeeding Women of childbearing potential (WOCBP) must agree to follow instructions for method(s) of contraception for the duration of treatment with study treatment and for 5 months post- treatment completion. Women should use an adequate method(s) of contraception Males who are sexually active with WOCBP must agree to follow instructions for method(s) of contraception for the duration of treatment with study treatment(s) and 7 months post-treatment completion. In addition, male participants must be willing to refrain from sperm donation during this time. Men who are sexually active with WOCBP must agree to follow instructions for method(s) of contraception Azoospermic males are exempt from contraceptive requirements. WOCBP who are continuously not heterosexually active are also exempt from contraceptive requirements, and still must undergo pregnancy testing as described in this section  Exclusion Criteria:  Active brain metastases or leptomeningeal metastases. Participants with brain metastases are eligible if these have been treated and there is no MRI evidence of progression for at least 4 weeks after treatment is complete and within 28 days prior to first dose of study treatment administration. 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 treatment administration. Stable dose of anticonvulsants is allowed. Treatment for central nervous system (CNS) metastases may include stereotactic radiosurgery (e.g. GammaKnife, CyberKnife, or equivalent) or neurosurgical resection. Patient who received whole brain radiation therapy are not eligible Subjects with interstitial lung disease that is symptomatic or may interfere with the detection or management of suspected drug-related pulmonary toxicity Uveal and mucosal melanoma are excluded Any condition including medical, emotional, psychiatric, or logistical that, in the opinion of the Investigator, would preclude the patient from adhering to the protocol or would increase the risk associated with study participation or study drug administration or interfere with the interpretation of safety results (eg, a condition associated with diarrhea or acute diverticulitis) 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 Participants with an active, known or suspected autoimmune disease. Participants with type I diabetes mellitus, hypothyroidism only requiring hormone replacement, skin disorders (such as vitiligo, psoriasis, or alopecia) not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll Participants with a condition requiring systemic treatment with either corticosteroids (> 10 mg daily prednisone equivalent) or other immunosuppressive medications within 14 days of start of week 1 day 1. Inhaled or topical steroids, and adrenal replacement steroid doses > 10 mg daily prednisone equivalent, are permitted in the absence of active autoimmune disease History of organ transplant or tissue that requires systemic use of immune suppressive agents Active infection requiring systemic therapy within 14 days prior to week 1 day 1  Known cardiac history including:  History of unstable or deteriorating cardiac disease within the previous 12 months prior to screening including but not limited to the following:  Unstable angina or myocardial infarction Transient ischemic attack (TIA)/cerebrovascular accident (CVA) Congestive heart failure (New York Heart Association [NYHA] class III or IV) Uncontrolled clinically significant arrhythmias Known history of positive test for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS). NOTE: Testing for HIV must be performed at sites where mandated locally Use of an investigational agent or an investigational device within 28 days before administration of first dose of study drug Participants who have received a live / attenuated vaccine within 30 days before first treatment Prior treatment with an anti-PD-1, anti-PD-L1, anti-PD-L2, or anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways with the exception of treatment with adjuvant intent Participants with history of life-threatening toxicity related to prior immune therapy (eg. anti- CTLA-4 or anti-PD-1/PD-L1 treatment or any other antibody or drug specifically targeting T- cell co-stimulation or immune checkpoint pathways) except those that are unlikely to re-occur with standard countermeasures (e.g.. hormone replacement after adrenal crisis) Treatment with botanical preparations (e.g., herbal supplements or traditional Chinese medicines) intended for general health support or to treat the disease under study within 2 weeks prior to study treatment initiation Whole blood cell (WBC) < 2000/uL (may not transfuse within 14 days of study treatment initiation) Neutrophils < 1500/uL (may not transfuse within 14 days of study treatment initiation) Platelets < 100,000/uL (may not transfuse within 14 days of study treatment initiation) Hemoglobin < 9.0 g/dL (may not transfuse within 14 days of study treatment initiation) Serum creatinine > 1.5 x upper limit of normal (ULN), unless creatinine clearance >= 40 mL/min (measured or calculated using the Cockcroft-Gault formula) Aspartate aminotransferase (AST)/alanine aminotransferase (ALT): > 3.0 x ULN Total bilirubin > 1.5 x ULN (except participants with Gilbert syndrome who must have a total bilirubin level of < 3.0 x ULN) Any positive test result for hepatitis B virus or hepatitis C virus indicating presence of virus, e.g., hepatitis B surface antigen (HBsAg, Australia antigen) positive, or hepatitis C antibody (anti-hepatitis C virus [HCV]) positive (except if HCV-ribonucleic acid [RNA] negative) History of allergy or hypersensitivity to study drug components History of severe hypersensitivity reaction to any monoclonal antibody Known hypersensitivity to tocilizumab, ipilimumab, or nivolumab Prisoners or participants who are involuntarily incarcerated. (Note: under certain specific circumstances a person who has been imprisoned may be included or permitted to continue as a participant Participants who are compulsorily detained for treatment of either a psychiatric or physical (e.g., infectious disease) illness