A Dose-Escalation Study to Evaluate the Safety, Tolerability, Pharmacokinetics, and Pharmacodynamics of IPI-549

Inclusion Criteria: All subjects must meet the following criteria for inclusion: * ≥ 18 years of age * Life expectancy of ≥ 3 months * Histological or cytological evidence of advanced and/or metastatic carcinoma or melanoma , excluding sarcoma * At least 1 measurable disease lesion as defined by RECIST 1.1 * Serum creatinine clearance ≥ 60 mL/min and serum creatinine ≤ 2.0 x the upper limit of normal (ULN) as determined by either of the following: Estimation as calculated by Cockcroft-Gault equation or Direct measurement by 24-hour urine collection * Total bilirubin ≤ 1.5 x ULN (unless elevated due to Gilbert's syndrome) * Aspartate aminotransferase (AST/SGOT) and alanine aminotransferase (ALT/SGPT) ≤ 2.5 x ULN (\<5x ULN if liver metastasis) * Adequate hematological function, defined as absolute neutrophil count ≥1.5 x 109/L, hemoglobin ≥ 9.0 g/dL, and platelet count ≥ 100 x 109/L * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 (corresponds to Karnofsky Performance Status (KPS) ≥ 60%) Subjects entering Part A, B, C, or D must also meet the following additional criterion: • Failure to respond to standard therapy, or for whom no appropriate therapies are available (based on the judgement of the Investigator) Subjects entering Part D, E, F or G must also meet the following additional criterion: • Willing to undergo 1 pre-treatment and 1 on-treatment tumor biopsy Subjects entering Part E must also meet the following additional criteria: * Histological or cytological evidence of NSCLC, melanoma, , human papillomavirus (HPV) positive or HPV negative SCCHN (oral cavity, pharynx, hypopharynx, larynx, nasopharyngeal \[including undifferentiated nasopharyngeal carcinoma\]), or another tumor type to be determined * Failure to respond to standard therapy, or for whom no appropriate therapies are available (based on the judgment of the Investigator The most recent treatment prior to study entry must be an anti-PD-1 or anti-PD-L1 antibody given as either monotherapy or in combination * Subjects with NSCLC Tumors that harbor an actionable genetic alteration for which there is a corresponding approved therapy for that specific alteration (including but not limited to alterations in EGFR, ALK, and ROS) must have progressed on, or had intolerance to, the respective therapy Subjects entering Part F must also meet the following additional criteria: * Histological or cytological evidence of estrogen-receptor negative (ER-), progesterone receptor negative (PgR-) and human epidermal growth factor-2 receptor negative (HER2-) Breast Cancer by local laboratory testing, based on last available tumor tissue; or another tumor type to be determined * ER/PgR negativity to follow local guidelines * If IHC HER2 2+, a negative FISH test is required * Inflammatory triple negative breast cancer is allowed * Must have received and failed/progressed a cytotoxic chemotherapy as first line therapy per standard of care * No prior anti-PD-1 or anti-PD-L1 therapy Subjects entering Part G must also meet the following additional criteria: * Histological or cytological evidence of ACC, mesothelioma, or another tumor type to be determined * Both pleural and peritoneal mesothelioma are allowed * Epithelioid, sarcomatoid, or biphasic mesothelioma subtypes are allowed * Progression after at least first line available therapy Patients entering Part H must also meet the following additional criteria: High-circulating MDSCs, currently defined for this study as MDSCs ≥ 20.5% as measured by CLIA-certified Serametrix assay Microsatellite status of tumor has been determined Patients with tumors that are microsatellite instability-high must have previously received an anti-PD-1/anti-PD-L1 therapy and progressed on therapy If patient's tumor type is one for which anti-PD-1/anti-PD-L1 therapy is standard of care, patient must have previously received an anti-PD-1 or anti-PD-L1 therapy and progressed while on that therapy Exclusion Criteria: Subjects are to be excluded from the study if they meet any of the following criteria: * Severe allergic or anaphylactic reaction to any monoclonal antibody therapy, murine protein, or known hypersensitivity to any excipient in the study drugs * Major surgery within 4 weeks prior to Screening * Subjects who have been treated with chemotherapy, biologic therapy, or other investigational agent within \< 5 times the half-life of the agent or \< 28 days (whichever is shorter) of starting study drug NOTE: Subjects whose immediate prior treatment was with nivolumab may start study drug 2 weeks after the last dose of nivolumab * Symptomatic or untreated brain metastases * Primary central nervous system (CNS) malignancy * Infection with human immunodeficiency virus (HIV), hepatitis B, or hepatitis C virus * Ongoing treatment with chronic immunosuppressants (eg, cyclosporine) or systemic steroids * Ongoing systemic bacterial, fungal, or viral infections at Screening NOTE: Subjects on antimicrobial, antifungal, or antiviral prophylaxis are not specifically excluded if all other inclusion/exclusion criteria are met * Administration of a live vaccine within 6 weeks of first dose of study drug * Administration of any of the following within 1 week prior to the administration of study drug: * Strong inhibitors or inducers of CYP3A4, including grapefruit products and herbal supplements * P-glycoprotein (P-gp) inhibitors * Warfarin, phenytoin, or other substrates of CYP2C8 or CYP2C9 with a narrow therapeutic range * Medications associated with QTc interval prolongation or Torsades de Pointes * Baseline QT interval corrected with Fridericia's method (QTcF) \> 480 ms (average of triplicate readings) NOTE: criterion does not apply to subjects with a right or left bundle branch block * Parts C, D-Annex, and E only: Subjects with active, known, or suspected autoimmune disease. Subjects with vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll * Prior surgery or gastrointestinal dysfunction that may affect drug absorption (eg, gastric bypass surgery, gastrectomy) * Concurrent active malignancy other than non-melanoma skin cancer, carcinoma in situ of the cervix, or prostate intraepithelial neoplasia * Past medical history of interstitial lung disease, drug-induced interstitial lung disease, radiation pneumonitis which required steroid treatment, or any evidence of clinically active interstitial lung disease * History of peptic ulcer and/or gastrointestinal bleed * History of stroke, unstable angina, myocardial infarction, or ventricular arrhythmia requiring medication or mechanical control within the last 6 months prior to Screening * Unstable or severe uncontrolled medical condition (eg, unstable cardiac function, unstable pulmonary condition including pneumonitis and/or interstitial lung disease, uncontrolled diabetes) or any important medical illness or abnormal laboratory finding that would, in the Investigator's judgment, increase the risk to the subject associated with his or her participation in the study.