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 outlined in Section 3.1 of MATCH Master Protocol (excluding Section 3.1.6) at the time of registration to treatment step (Step 1, 3, 5, 7)
* Patients must have complete loss of cytoplasmic and nuclear PTEN by immunohistochemistry (ICH) as determined via the MATCH Master Protocol and described in Appendix I. Patients can have any PTEN mutation or deletion status, but MUST have PTEN loss by IHC
* 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 hemoglobulin (Hb) A1c ≤ 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 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 ≥ 100x10\^9 /L
* Hemoglobulin (Hgb) \> 9 g/dl
* Total serum bilirubin \< 2.0 mg/dL
* Aspartate aminotransferase (ALT) and Alanine aminotransferase (AST) \< 2.5 x 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, CMV PCR can be obtained at the discretion of treating physician or local institutional guidelines
* Patients must agree not to conceive or father children by agreeing to use contraception while receiving study treatment and for 1 month after the last dose of copanlisib
