Comparing Standard of Care Chemotherapy Treatment to the Combination of Copanlisib and Olaparib for Recurrent Platinum Resistant Ovarian Cancer That Has Progressed Through PARP Inhibitor Therapy

Inclusion Criteria:

* Patients with recurrent ovarian cancer. Ovarian cancer = fallopian tube cancer, ovarian cancer, primary peritoneal cancer. The following histology types are eligible:

  * High grade serous
  * Endometrioid, grade 3
  * Any histology with BRCA1 and/or BRCA2 deleterious mutation (germline or somatic)

    * Histologic confirmation of the original primary tumor is required via the pathology report (upload of report required)
    * Confirmation of BRCA1 and BRCA2 germline status is required for all entered patients (upload of report\[s\] required)
    * Tumor/somatic genomic testing can be provided or entered as not done (upload of report\[s\] required)
    * Homologous recombination deficiency (HRD) testing can be provided or entered as not done (upload of report\[s\] required)
    * Genetic/genomic testing results and HRD testing results, initially entered as not done, should be uploaded if they become available anytime during conduct of the study
* Participants must have progressed by imaging while receiving PARP inhibitor therapy (irrespective of whether PARP inhibitor therapy was given as maintenance therapy or as primary recurrence therapy); rising CA125 only is not considered as evidence of progression
* Platinum-resistant disease, defined as progression within \< 6 months from completion of platinum-based therapy, and inclusive of platinum refractory disease. The date should be calculated from the last administered dose of platinum therapy
* Unlimited lines of cytotoxic therapy allowed in the platinum-sensitive setting; =\< 2 lines of cytotoxic therapy allowed in the platinum-resistant setting

  * Hormonal therapy (e.g., tamoxifen, aromatase inhibitors) will not count as a previous line of therapy
* Prior use of bevacizumab in the upfront or recurrent setting is required
* Participants must have evaluable disease - defined as RECIST 1.1 measurable disease OR non-measurable disease (defined as solid and/or cystic abnormalities on radiographic imaging that do not meet RECIST 1.1 definitions for target lesions OR ascites and/or pleural effusion that has been pathologically demonstrated to be disease-related in the setting of a CA125 \> 2 x upper limit of normal \[ULN\])
* Age \>= 18
* Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 or 2
* Absolute neutrophil count (ANC) \>= 1,500/mcl (within 14 days prior to registration)
* Hemoglobin \>= 10 g/dL (within 14 days prior to registration)
* Platelets \>= 100,000/mcL (within 14 days prior to registration)
* Creatinine clearance (CrCL) \>= 51 mL/min (estimated using Cockcroft-Gault equation) (within 14 days prior to registration)
* Total serum bilirubin level =\< 1.5 x ULN (patients with known Gilbert's disease who have bilirubin level =\< 3 x ULN may be enrolled) (within 14 days prior to registration)
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3 x ULN (within 14 days prior to registration)
* Lipase =\< 1.5 x ULN within 14 days of registration
* International normalized ratio (INR) =\< 1.5 x ULN (or an in-range INR, usually between 2 and 3, if a patient is on a stable dose of therapeutic warfarin) and a partial thromboplastin time (PTT) =\< 1.5 times the upper limit of normal within 14 days of registration
* 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
* Patients who are therapeutically treated with an agent such as warfarin or heparin will be allowed to participate provided that their medication dose and INR/PTT is stable. Oral anticoagulants are allowed provided there are no interactions
* The effects of copanlisib and olaparib on the developing human fetus are unknown. For this reason and because maternal toxicity, developmental toxicity and teratogenic effects have been observed in nonclinical studies and PI3K inhibitors agents as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation, and for 1 month after the last dose of copanlisib and/or olaparib. Should a woman become pregnant or suspect she is pregnant while she is participating in this study, she should inform her treating physician immediately
* 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
* Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months of registration are eligible for this trial
* Patients with evidence of chronic hepatitis B virus (HBV) infection must have an undetectable HBV viral load 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 treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression and must be off steroids and stable at least one month
* The patient or a legally authorized representative must provide study-specific informed consent prior to study entry and, for patients treated in the United States (U.S.), authorization permitting release of personal health information

Exclusion Criteria:

* Prior therapy:

  * No chemotherapy or radiotherapy within 4 weeks of registration
  * No hormonal therapy within 2 weeks of registration. Patients receiving raloxifene for bone health as per Food and Drug Administration (FDA) indication may remain on raloxifene absent other drug interactions
  * No investigational agents within 4 weeks of registration
  * No prior PI3K-AKT-mTOR pathway inhibitor therapy
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to olaparib, copanlisib, or other agents used in this study
* Copanlisib and olaparib are primarily metabolized by CYP3A4. Therefore, the concomitant use of strong inhibitors of CYP3A4 (e.g., ketoconazole, itraconazole, clarithromycin, ritonavir, indinavir, nelfinavir and saquinavir), and strong inducers of CYP3A4 (e.g., rifampin, phenytoin, carbamazepine, phenobarbital, St. John's Wort) are not permitted from 14 days prior to registration until the end of the study
* Systemic corticosteroid therapy at a daily dose higher than 15 mg prednisone or equivalent is not permitted while on study. Patients may be using topical or inhaled corticosteroids
* Use of concomitant herbal medications/preparations (except for vitamins), alternative/complimentary medications, immunosuppressive therapy, or other prohibited medications
* Patients with uncontrolled type I or II diabetes mellitus; uncontrolled diabetes is defined as glycosylated hemoglobin (HbAlc) \> 8.5%
* Patients with arterial or venous thrombotic or embolic events such as cerebrovascular accident (including transient ischemic attacks), deep vein thrombosis, or pulmonary embolism within 3 months before registration
* Gastrointestinal conditions that would preclude consumption (swallowing), retention, and/or absorption of oral medications
* Patients with drainage gastrostomy tube are not allowed
* Patients with dependency on IV hydration or total parenteral nutrition (TPN) are not allowed
* Patients with uncontrolled intercurrent illness, including but not limited to:

  * Persistent grade \>= 2 adverse events due to prior anti-cancer therapy with the exception of alopecia, hypothyroidism requiring medication, vitiligo, and the laboratory values defined in the inclusion criteria.
  * Known psychiatric illness/social situations that would limit compliance with study requirements.
  * History of or current autoimmune disease
  * Non-healing wound, ulcer, or bone fracture
  * Active, clinically serious infections \> grade 2 (CTCAE v5.0)
* Women who are pregnant or unwilling to discontinue nursing
* Patients who have a history of non-infectious pneumonitis/interstitial lung disease (ILD) that required steroids, or current non-infectious pneumonitis/ILD