• Patients must have histologically confirmed solid malignancy that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective.

• For the dose escalation and dose expansion phases, patients must have genomic evidence of inactivating ATM mutations, amplification of MYC, mutation of FBXW7, CCNE1 amplification, SWI/SNF member mutation (ARID1A, PBRM1, SMARCA4, ARID2, ARID1b, SMARCA2, SS18), and ATRX/DAXX. Other SWI/SNF mutations may be considered after discussion with the principal investigator (PI).

• Progression on at least one prior standard therapy.

• Age \>= 18 years. Because no dosing or adverse event data are currently available on the use of peposertib (M3814) in combination with M1774 in patients \< 18 years of age, children are excluded from this study.

• Life expectancy \> 3 months.

• Eastern cooperative oncology group (ECOG) performance status =\< 2 (Karnofsky \>= 60%).

• Measurable disease by response evaluation criteria in solid tumors (RECIST) 1.1 (RECIST) 1.1 non-measurable disease permitted for the dose escalation portion).

• Hemoglobin \>= 9 g/dL.

• Absolute neutrophil count \>= 1,500/mcL.

• Platelets \>= 1000,000/mcL.

• Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN).

• Asparate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]/alanine aminotransferase (ALT)(serum glutamic pyruvic transaminase \[SGPT\]) =\< 3 × institutional ULN or =\< 5.0X the ULN if liver metastases are present.

• Glomerular filtration rate (GFR) \>= 60 mL/min/1.73m\^2.

• Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial. Anti-retroviral therapy agents must be considered for potential drug-drug interactions per exclusion.

• For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated.

• Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load.

• Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial.

• Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better.

• Able to swallow whole capsules or tablets.

• Willing to undergo paired biopsies (expansion arm).

• Female patients of childbearing potential must have a negative urine or serum pregnancy test within 72 hours prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required.

‣ Female patients of childbearing potential must be willing to use an adequate method of contraception for the course of the study through 6 months after the last dose of study medication.

⁃ Male patients of reproductive potential must agree to avoid impregnating a partner while receiving study drug and for 3 months after the last dose of study drug by complying with adequate methods of contraception.

⁃ Note: Abstinence is acceptable if this is the usual lifestyle and preferred contraception for the patient.

• Ability to understand and the willingness to sign a written informed consent document. Participants with impaired decision-making capacity who have a legally-authorized representative (LAR) and/or family member available will also be eligible.