Testing the Combination of DS-8201a and Olaparib in HER2-Expressing Cancers With Expansion in Patients With Platinum Resistant Ovarian Cancer

Inclusion Criteria: * DOSE ESCALATION PHASE: * Patients must have histologically confirmed malignancy that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective * Patients must have HER2-positive or HER2-expressing tumors determined by a Clinical Laboratory Improvement Act (CLIA)-certified laboratory. Specific requirement of HER2 status is outlined below: * Dose Escalation Module 1 and Module 2: * HER2 1-3+ expression by IHC OR * HER2 amplification by next generation sequencing panel (NGS) or in situ hybridization (ISH) OR * If local testing is not feasible, patients will submit archival tissue for central HER2 testing to determine eligibility. Patients with unknown or negative HER2 testing will not be eligible * Dose Escalation Module 3: * HER2 1-2+ expression by IHC OR * HER2 amplification by next generation sequencing panel (NGS) or in situ hybridization (ISH) OR * If local testing is not feasible, patients will submit archival tissue for central HER2 testing to determine eligibility. Patients with unknown or negative HER2 testing will not be eligible * DOSE EXPANSION PHASE: * Patients must have histologically confirmed platinum resistant, high grade serous ovarian carcinoma. Platinum resistant is defined as radiographic progression \< 6 months following the last dose of platinum therapy * HER2 IHC 1+ per local or central testing * There must be least one lesion suitable for biopsy without significant risk to the patient * Patient disease must be evaluable or measurable by Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1. Biopsiable lesion cannot be the only RECIST-measurable lesion * DOSE ESCALATION AND DOSE EXPANSION PHASES: * Patients must have had at least one prior line of cytotoxic chemotherapy * Patients can have received an unlimited number of additional lines of chemotherapy, targeted therapy, biologic therapy, or hormonal therapy * Patients must have archival formalin-fixed paraffin-embedded (FFPE) tissue available for central confirmation of HER2 testing * Age \>= 18 years. Because no dosing or adverse event data are currently available on the use of DS-8201a in combination with olaparib in patients \< 18 years of age, children are excluded from this study * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%) * Hemoglobin \>= 10.0 g/dL (within 21 days of randomization/enrollment) * No transfusions with red blood cells or platelets are allowed within 1 week prior to screening assessment * Absolute neutrophil count \>= 1,000/mcL (within 21 days of randomization/enrollment) * No administration of granulocyte colony-stimulating factor (G-CSF) is allowed within 1 week prior to screening assessment * Platelets \>= 100,000/mcL (within 21 days of randomization/enrollment) * No transfusions with red blood cells or platelets are allowed within 1 week prior to screening assessment * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN), (\< 3 x ULN in the presence of documented Gilbert's syndrome or liver metastases at baseline) (within 21 days of randomization/enrollment) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional ULN (within 21 days of randomization/enrollment) * Creatinine =\< 1.5 x institutional ULN OR glomerular filtration rate (GFR) \>= 51 mL/min/1.73 m\^2 unless data exists supporting safe use at lower kidney function values, no lower than 30 mL/min/1.73 m\^2 (using the Cockcroft-Gault Equation) (within 21 days of randomization/enrollment) * Patients must have left ventricular ejection fraction (LVEF) \>= 50% by either an echocardiogram (ECHO) or multigated acquisition (MUGA) scan within 28 days before randomization/enrollment * Patients who are human immunodeficiency virus (HIV) positive may participate IF they meet the following eligibility requirements: * They must be stable on their anti-retroviral regimen, and they must be healthy from an HIV perspective * They must have an undetectable viral load and a CD4 count \>= 250 cells/uL within 7 days of enrollment * They must not be currently receiving prophylactic therapy for an opportunistic infection and must not have had an opportunistic infection within the past 6 months * HIV-infected patients should be monitored every 12 weeks for viral load and CD4 counts * 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 brain metastases should be stable and off steroids and at least 4 weeks from radiation at the time of registration * 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 better than class 2B * The effects of DS-8201a and olaparib on the developing human fetus are unknown. For this reason and because HER2 antibody conjugated to a topoisomerase 1 inhibitor agents as well as PARP inhibitors are known to be teratogenic; thus, women of child-bearing potential and men must agree to use highly effective contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of st