Inclusion Criteria:
* Patients must have met applicable eligibility criteria in the Master MATCH Protocol EAY131/ NCI-2015-00054 prior to registration to treatment subprotocol
* Patients must fulfill all eligibility criteria of MATCH Master Protocol at the time of registration to treatment step (Step 1, 3, 5, 7)
* Patients must have mutations in the PTEN gene with 1% or more expression of PTEN by immunohistochemistry (IHC) as determined via the MATCH Master Protocol
* NOTE: For patients entering the study, all patients must have PTEN IHC performed as described in the MATCH Master Protocol. This includes patients entering the study via the outside assay process
* Patients must not have co-existing aberrations in the MAPK or PI3K/MTOR pathways as determined by the MATCH screening assessment in NRAS, HRAS, KRAS, BRAF, PIK3CA, AKT or mTOR
* 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 must not have known hypersensitivity to copanlisib or compounds of similar chemical or biologic composition
* Patients must not have had prior treatment with copanlisib or other PI3K inhibitors, AKT inhibitors or mTOR inhibitors
* 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 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 a glycosylated hemoglobin (HbA1c) ≤ 8.5% within 28 days from registration
* Patients must not have uncontrolled hypertension defined as systolic blood pressure (SBP) greater than 160 mmHg or diastolic blood pressure (BP) greater than 100 mmHg or use of more than 2 anti-hypertensive medications
* Patients must not have HER2 positive (3+ by IHC or fluorescence in situ hybridization \[FISH\] ratio ≥ 2) breast cancer
* Patients must not have indolent NHL (non-Hodgkin's lymphoma) or DLBCL (diffuse large B cell lymphoma) because other studies are ongoing with this agent in this group of patients
* Patients must not be on anti-arrhythmic therapy other than digoxin or beta-blockers
* Absolute neutrophil count (ANC) ≥ 1.5 x 10\^9 /L
* Platelets ≥ 100 x10\^9 /L
* Hemoglobin (Hb) \> 9 g/dl
* Total serum bilirubin \< 2.0 mg/dL
* Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \< 2.5x upper limit of normal (ULN) (\< 5 x ULN in patients with liver metastases)
* Serum creatinine \< 1.5 x ULN
* 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
* 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
