Copanlisib With Dose-Adjusted EPOCH-R in Relapsed and Refractory Burkitt Lymphoma and Other High-Grade B-cell Lymphomas

Background: Burkitt Lymphoma (BL) and diffuse large B-cell lymphoma (DLBCL) are aggressive B cell lymphomas. Frontline treatment does not always work. Researchers want to see if a combination of drugs can help. Objective: To learn if it is safe to give people with certain cancers copanlisib together with rituximab and combination chemotherapy dose-adjusted etoposide, prednisone, vincristine, cyclophosphamide, doxorubicin, and rituximab (DA-EPOCH-R). Eligibility: People ages 18 and older with relapsed and/or refractory highly aggressive B-cell lymphomas such as BL and certain types of diffuse large B-cell lymphoma (DLBCL). Design: Participants will be screened with: Medical history Physical exam Bone marrow aspiration and biopsy. A needle will be put into their hipbone. Marrow will be removed. Imaging scans of the chest, abdomen, pelvis, and/or brain Tumor biopsy (if needed) Blood and urine tests Heart function tests Treatment will be given in 21-day cycles for up to 6 cycles. Participants will get copanlisib by intravenous (IV) infusion. They will also get a group of medicines called DA-EPOCH-R, as follows. They will get rituximab by IV infusion. Doxorubicin, etoposide, and vincristine will be mixed together in an IV bag and given by continuous IV infusion over 4 days. They will get cyclophosphamide by IV infusion. They will take prednisone by mouth. Participants will have frequent study visits. At these visits, they will repeat some screening tests. They may give tissue, saliva, and cheek swab samples. They will have at least one spinal tap. For this, a needle will be inserted into the spinal canal. Fluid will be removed. Participants will have a visit 30 days after treatment ends. They will have follow-up visits for at least 5 years.