Inclusion Criteria:  Provision of written informed consent prior to any study related procedures Patients >= 18 years of age at the time of study entry who agree to participate by giving written informed consent prior to participation in any study related activities  Histologically or cytologically confirmed advanced solid tumors, specifically,  Dose Escalation and Dose Expansion may include:  Patients with tumors with actionable KEAP1/NFE2L2/STK11/NF1 mutations Patients with low ASNS expression levels (high-grade serous ovarian carcinoma [HGSOC] or endometrial cancer) Post-immunotherapy (IO) melanoma (minimum treatment duration of prior PD-1 or PD-L1-containing regimen is 12 weeks [or equivalent of 2 response evaluations])  Dose Escalation may also include:  Patients with post-platinum HNSCC Patients with chondrosarcoma Patients with ARID1A mutant clear cell ovarian cancer Note: all biomarker mutations/expression levels must be confirmed prior to study treatment Patients must have received at least one line of therapy for advanced stage disease and be refractory or ineligible to available existing therapy(ies) known to provide clinical benefit for their condition Prior treatment with chemotherapy, radiotherapy, immunotherapy or any investigational therapies must have been completed at least 3 weeks or at least five half-lives, whichever is shorter, before the study drug administration, and all adverse events (AEs) (excluding alopecia and peripheral neuropathy) have either returned to =< grade 1 or stabilized Fresh and/or archival tumor tissue from the biopsy obtained between the completion of the most recent line of treatment until study entry must be available for mutation and biomarker analysis. Patients should not be put at undue risk to obtain fresh tumor biopsy. If available, archival tumor tissue from time of initial diagnosis will be collected in addition to the most recent biopsy (archival and/or fresh) Measurable or non-measurable evaluable disease as defined per the Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1 (or immune-related RECIST [iRECIST] for Part B only) Eastern Cooperative Oncology Group (ECOG) performance status =< 1 Absolute neutrophil count (ANC) >= 1500/mL Platelets >= 100,000/mL Hemoglobin >= 9 g/dL Serum creatinine =< 1.5 x upper limit of normal (ULN) and/or creatinine clearance > 40 mL/min. Actual body weight should be used for calculating creatinine clearance using the Cockroft-Gault equation (except for patients with body mass index > 30 kg/m^2 when the lean body weight should be used) Serum total bilirubin =< 1.5 x ULN (with the exception of patients with known Gilbert's syndrome: serum total bilirubin must be < 3 x ULN in these patients) Aspartate aminotransferase (serum glutamic oxaloacetic transaminase) and alanine aminotransferase (serum glutamic pyruvic transaminase) =< 2.5 x ULN or =< 5 x ULN for patients with liver metastases) Left ventricular ejection fraction >= 50%  Female patients are eligible to enter and participate in the study if they are of:  Non-childbearing potential (physiologically incapable of becoming pregnant), including any female who:  Has had a hysterectomy, OR Has had a bilateral oophorectomy, OR Has had a bilateral salpingectomy, OR Is postmenopausal (total cessation of menses for >= 2 years, or follicle-stimulating hormone >= 50 IU/L)  Childbearing potential, but with a negative serum pregnancy test at screening (within 7 days of the first investigational medicinal product [IMP] administration), is not breastfeeding, and uses highly effective contraception at study entry and throughout the study until 90 days after the last administration. Highly effective contraceptive methods include:  Combined (estrogen and progestogen containing) hormonal contraception associated with inhibition of ovulation (for example oral, intravaginal, transdermal) Progestogen-only hormonal contraception associated with inhibition of ovulation (for example oral, implantable, injectable) Intrauterine device Intrauterine hormone-releasing system Bilateral tubal occlusion Male partner has had a vasectomy Male patients are eligible to enter and participate in the study if they agree to use effective methods of contraception during the study treatment period and for at least 90 days after the last dose of investigational product  Exclusion Criteria:  Prior malignancy within the previous 2 years except for locally curable cancers that have been cured, such as basal or squamous cell skin cancer, or carcinoma in situ of the cervix, breast or bladder  Known primary central malignancy or symptomatic central nervous system metastasis(es)  Note: Patients with stable, previously treated brain metastases may participate if neurologic symptoms have resolved, patients have been off steroids for at least 7 days, and there is no evidence of disease progression by imaging for at least 2 weeks before the first dose of study treatment Patients should be excluded if they have a condition requiring systemic treatment with either corticosteroids (> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 2 weeks of the first dose of study drug  Uncontrolled, significant intercurrent or recent illness including, but not limited to, the following cardiac conditions:  Any unstable cardiac arrhythmia within 6 months prior to enrolment Prolongation of the Fridericia corrected QT (QTcF) interval defined as > 450 ms for males and > 470 ms for females  History of any of the following cardiovascular conditions within 6 months of enrolment:  Cardiac angioplasty or stenting, myocardial infarction, unstable angina, coronary artery Bypass graft surgery, symptomatic peripheral vascular disease, class III or IV congestive heart failure, as defined by the New York Heart Association Major surgical intervention within 28 days before study drug administration Significant acute or chronic infections Any psychiatric condition that would prohibit the understanding or rendering of informed consent Treatment with strong cytochrome P450 (CYP450) subtype 3A4 (CYP3A4) inducers (including St John's wort) and inhibitors (including grapefruit juice) within 7 days of the first dose of study drug Treatment with strong CYP450 subtype 2D6 (CYP2D6) inhibitors within 7 days of the first dose of study drug Radiotherapy within 4 weeks prior to the start of study drug. Palliative radiotherapy for symptomatic control is acceptable if completed at least 2 weeks prior to study drug administration and no additional radiotherapy for the same lesion is planned Underlying medical conditions that, in the investigator's opinion, will make the administration of study drug hazardous or obscure the interpretation of toxicity determination or AEs History of allergic reactions attributed to compounds of similar chemical or biological composition to any of the compounds in the study Known alcohol or drug abuse Legal incapacity or limited legal capacity Inability to swallow oral medications (capsules and tablets) without chewing, breaking, crushing, opening or otherwise altering the product formulation. Patients should not have gastrointestinal illnesses that would preclude the absorption of IACS-6274, which is an oral agent Patients unwilling to comply with protocol requirements related to the assigned part PART B (DOSE ESCALATION AND DOSE EXPANSION) SPECIFIC EXCLUSION CRITERIA Autoimmune disease that might deteriorate when receiving an immune-stimulatory agent, or immunodeficiencies Known severe hypersensitivity reactions to monoclonal antibodies, any history of anaphylaxis, or uncontrolled asthma (that is, three or more features of partially controlled asthma) Prior organ transplantation, including allogeneic stem cell transplantation Patient has received a live vaccine within 30 days prior to the first dose of study drug. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guerin and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist) are live attenuated vaccines and are not allowed