Inclusion Criteria:
* Patients must have met applicable eligibility criteria in the Master MATCH Protocol prior to registration to treatment subprotocol
* Patients must have PIK3CA mutation as determined via the MATCH Master Protocol
* Patients must have an electrocardiogram (ECG) within 8 weeks prior to treatment assignment and must have no clinically important abnormalities in rhythm, conduction or morphology of resting ECG (e.g. complete left bundle branch block, third degree heart block)
* Patients should stop using herbal medications at least 7 days prior to the first dose of copanlisib. Herbal medications include, but are not limited to: St. John's Wort, Kava, ephedra, gingko biloba, dehydroepiandrosterone (DHEA), yohimbe, saw palmetto, black cohosh and ginseng
* Patients with type I or II diabetes mellitus must have glycosylated hemoglobin A1c (HbA1c) =\< 8.5% within 28 days from registration
* Absolute neutrophil count (ANC) \>= 1.5 x 10\^9 /L
* Platelets \>= 100x10\^9/L
* Hemoglobin (Hb) \> 9 g/dl
* Total serum bilirubin \< 2.0 mg/dL
* Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \< 2.5 x upper limit of normal (ULN) (\< 5 x ULN in patients with liver metastases)
* Serum creatinine \< 1.5 x ULN
* Men and women of child-bearing potential must agree to use contraception while receiving study treatment and for 1 month after the last dose of copanlisib
Exclusion Criteria:
* Patients must not have known hypersensitivity to copanlisib or compounds of similar chemical or biologic composition
* Patients must not have had prior therapy with copanlisib or other PI3K inhibitors, AKT inhibitors or mTOR inhibitors
* Patients must not have activating KRAS mutations
* Patients must not have HER2 positive (3+ by immunohistochemistry \[IHC\] or fluorescence in situ hybridization \[FISH\] ratio \>= 2) breast cancer
* Patients must not have indolent non-Hodgkin lymphoma (NHL) (follicular lymphoma, small lymphocytic lymphoma \[SLL\]/chronic lymphocytic leukemia \[CLL\], lymphoplasmacytic lymphoma \[LPL\], marginal zone lymphoma) or DLBCL (diffuse large B cell lymphoma)
* Patients must not be on strong inhibitors or inducers of CYP3A4 within two weeks prior to start of study treatment and for the duration of study treatment
* Patients must not be on anti-arrhythmic therapy other than digoxin or beta-blockers
* Patients with non-healing wound, ulcer, or bone fracture are not eligible
* Patients with history of or current interstitial pneumonitis are not eligible
* NOTE: For solid tumors, cytomegalovirus (CMV) polymerase chain reaction (PCR) can be obtained at the discretion of treating physician or local institutional guidelines
