Testing the Addition of a New Anti-cancer Drug, Venetoclax, to Usual Chemotherapy for High Grade B-cell Lymphomas

Inclusion Criteria: * Pathologic diagnosis of diffuse large B-cell lymphoma (DLBCL) or high grade B-cell lymphoma not otherwise specified (HGBCL not otherwise specified \[NOS\]). Eligible subtypes include DLBCL NOS, Epstein Barr Virus positive (EBV+) DLBCL, HGBCL NOS and DLBCL/HGBCL transformed from an underlying indolent B-cell lymphoma. Patients with T-cell/histiocyte rich large B-cell lymphoma and primary mediastinal B-cell lymphoma are not eligible * Double hit lymphoma (DHL) or double expressing lymphoma (DEL) * DHL is defined as high grade B-cell lymphoma with one of the below: * Translocations of MYC and BCL2 * Translocations of MYC and BCL2 and BCL6 (triple hit lymphoma) * Translocations of MYC and BCL6 without BCL2 translocation BUT with immunohistochemistry (IHC) expression of BCL2 (\>=50%) * DEL is defined as DLBCL or high grade B-cell lymphoma not otherwise specified (NOS) with protein expression by IHC of both MYC (\>= 40%) and BCL2 (\>= 50%) in the absence of dual translocations of both MYC and BCL2 and/or BCL6). (Double Expressing Lymphoma, DEL). Local determination of fluorescence in situ hybridization (FISH) and IHC will be performed per standardized guidelines and will be acceptable for study entry, but local IHC and FISH results for MYC must be submitted for central review in order to determine eligibility if enrolling as DEL based on local results during phase II. Central pathology review is no longer required as of Update #03. * The dia…