Patient must be deemed eligible to proceed with high-dose chemotherapy and autologous stem cell transplantation by local transplant center At least weeks from autologous stem cell transplantation Patients who completed single autologous stem cell transplant after completion of at most induction regimens (excluding dexamethasone alone) and are in at least stable disease compared to pre-induction in the first days after stem cell transplantation For rituximab in combination with polatuzumab vedotin and lenalidomide (R + Pola + Len) treatment group: R/R DLBCL after treatment with at least one prior chemoimmunotherapy regimen that included an anti-CD monoclonal antibody in patients who are not eligible for autologous stem-cell transplantation or who have experienced disease progression following treatment with high-dose chemotherapy plus autologous stem-cell transplantation Institutional criteria for and have institutional approval to undergo autologous peripheral blood stem cell transplantation NOTE: There is no limit to the prior number of chemotherapy regimens; patients with prior autologous or allogeneic stem cell transplantation, as well as prior therapy with cyclophosphamide or alemtuzumab, are eligible Receipt of any organ transplantation including autologous or allogeneic stem-cell transplantation. One or more prior lines of chemoimmunotherapy and/or monotherapy with rituximab or other anti-cluster of differentiation (CD) antibody; patients may have had a prior autologous stem cell transplant but not prior allogeneic stem cell transplantation Deemed eligible for autologous stem cell transplantation (ASCT) by standard institutional criteria Cohort #: considered eligible for high-dose chemotherapy followed by autologous stem cell transplantation (ASCT) High-dose chemotherapy followed by stem cell transplantation (autologous or allogeneic). Prior autologous or allogeneic stem cell transplantation High dose chemotherapy followed by autologous stem cell transplantation within days prior to initiating study treatment; Patients who are candidate for an autologous or allogeneic stem cell transplantation (SCT) will be allowed to receive the study drugs as a bridge to transplantation if candidates for transplant Patients with HL or DLBCL must refuse or not be candidates for curative autologous stem cell transplantation Received prior autologous stem cell transplantation as first line therapy for multiple myeloma with subsequent disease relapse/progression Candidate for second autologous stem cell transplantation per local institutions guidelines with at least x ^/kg CD+ autologous stem cells available for transplantation More than one prior transplant prior to study entry with the exception of tandem transplantation; tandem transplantation is defined as two autologous stem cell transplants that occur within months of one another, and the patient did not have disease progression in the period between the two transplants Prior autologous or allogeneic stem cell transplantation Prior treatment with chimeric antigen receptor (CAR) T cells or other forms of adoptive cellular therapy, with the exception of autologous stem cell transplantation Autologous stem cell transplantation within weeks before the starting IP treatment or past history of allogeneic stem cell transplantation. Patient participants who have undergone autologous stem cell transplantation (autoSCT) are eligible provided that they are >= weeks from stem cell infusion Autologous stem cell transplantation within weeks prior to study entry Diagnosis of multiple myeloma undergoing planned autologous stem cell transplantation Not suitable for, or declined high dose chemotherapy and autologous stem cell transplantation (ASCT). Prior autologous stem cell transplantation. Have undergone organ transplantation including allogeneic or autologous stem-cell transplantation, at any time; Patients who have undergone autologous stem cell transplantation within months from study entry Tandem autologous transplantation Patients who have undergone prior autologous stem cell transplantation or allogeneic transplantation Patients must have undergone autologous stem cell transplantation, within months of initiation of induction therapy for newly diagnosed myeloma Prior allogeneic or autologous transplantation Transplantation for AML (allogeneic or autologous) allowed unless within days of study entry Patients should have received single autologous stem cell transplantation - days prior to enrollment to the trial Patients must be eligible to undergo autologous stem cell transplantation by standard institutional criteria History of bone marrow or stem cell transplantation (allogeneic or autologous) Prior high dose chemotherapy with autologous stem cell transplant, or prior allogeneic transplantation Multiple myeloma with disease in the following categories:\r\n* Patients with relapsed multiple myeloma following autologous stem cell transplantation who have achieved at least partial response following additional chemotherapy\r\n* Patients with high risk cytogenetics at diagnosis must have achieved at least a partial response following autologous stem cell transplantation; patients must have complex karyotype, delp, t; and/or t; by fluorescent in situ hybridization (FISH) and/or del by karyotyping Prior autologous or allogeneic hematopoietic cell transplantation (other than autologous SCT - days prior to registration) Time available (at least weeks) for treatment of hepatitis C prior to autologous or allogeneic transplantation Prior autologous or allogeneic transplantation for any disease Autologous stem cell transplantation less than days prior to study day History of organ or previous autologous/allogeneic stem cell transplantation Prior hematopoietic cell transplantation allogeneic or autologous (A prior autologous HCT will be allowed as long as it was part of tandem transplantation). Patients who have undergone autologous stem cell transplantation (ASCT) are eligible provided that they are >= weeks from stem cell infusion and meet other eligibility criteria Eligible for autologous transplantation Previous stem cell collection or transplantation (autologous or allogeneic) Patients who have undergone autologous or allogeneic stem cell transplantation Completion of, if applicable, an autologous stem cell transplantation (ASCT) at least months prior to first dose of study drug. Has received autologous stem cell transplantation (ASCT) within weeks before the date of randomization. Subject must have documented diagnosis with previously untreated (for cohort C, the induction and consolidation treatment along with the first Autologous stem cell transplantation (ASCT) are allowed), symptomatic Multiple Myeloma (MM) as defined by the criteria below: Patients must NOT have received autologous or allogeneic stem cell transplantation Eligible for autologous stem cell transplantation Patients are eligible >= weeks after autologous stem cell transplants or stem cell infusions as long as hematologic and other eligibility criteria have been met Prior stem cell transplantation allogeneic or autologous For rituximab + Atezo + Pola treatment group: relapsed or refractory DLBCL after treatment with at least one prior chemoimmunotherapy regimen that included an anti-CD monoclonal antibody, in participants who are not eligible for second line combination (immuno-) chemotherapy and autologous stem-cell transplantation or who have failed second line combination (immuno-) chemotherapy or experienced disease progression following autologous stem-cell transplantation Eligible for autologous stem cell transplantation Has received high dose chemotherapy followed by autologous stem cell transplantation less than days prior to first dose of study treatment Prior stem cell transplantation (autologous or allogeneic) Research participant has an indication to be considered for autologous stem cell transplantation Prior solid organ transplantation or allogenic stem cell transplantation (ASCT). However, previous autologous BM transplant (ABMT) or autologous peripheral blood stem cell transplant (PBSCT) is permitted. Patient is considered for autologous stem cell transplantation with full dose melphalan ( mg/m^) Patients previously treated with autologous or allogeneic bone marrow or stem cell transplantation are ineligible Patients with relapsed multiple myeloma following autologous stem cell transplantation who achieved < partial response following additional chemotherapy or who achieved < partial response (PR) at months following autologous stem cell transplantation and patients with plasma cell leukemia at diagnosis Patient must have undergone autologous stem cell transplantation, with melphalan as a preparative regimen, within months of initiation of induction therapy for newly diagnosed myeloma Patients who are eligible for autologous transplantation Patients with prior autologous stem cell transplants will be included; patients with prior allogeneic stem cell transplants will be eligible for nd BMT if not previously transplanted with FLT on -c- Progressive disease within weeks of prior therapy or within weeks after prior autologous stem cell transplantation Greater than approximately months since autologous stem cell transplantation Patients who have undergone autologous/allogeneic stem cell transplantation are eligible Patients who are candidates for autologous stem-cell transplantation due to primary refractory or first relapse of disease Patients with newly diagnosed double hit in first complete remission, anytime during the first months after chemoimmunotherapy followed by autologous stem cell transplantation if there was no evidence of progression Less than month since completion of autologous stem cell transplantation or less than months since completion of allogeneic stem cell transplantation Must be eligible for autologous transplantation according to institutional guidelines Prior autologous or allogeneic stem cell transplantation Eligible for autologous transplantation Previous autologous stem cell collection Eligible for autologous stem cell transplantation Previous autologous or allogeneic stem cell transplantation. Patients must have relapsed or progressed after at least one prior cytotoxic chemotherapy\r\n* Previous autologous or allogeneic stem cell transplantation is permitted\r\n* Previous treatment with either single agent panobinostat or lenalidomide is permitted Patients who are candidates for high dose chemotherapy and autologous stem cell transplantation with curative intent should not be enrolled Previous allogeneic stem cell transplantation at any time OR autologous stem cell transplantation within months of study entry. Previous autologous stem cell transplantation within months prior to randomization. At the discretion of the principal investigator if he/she feels that the patient is unable to safely complete the study; specifically, patients must be considered medically eligible to undergo high dose chemotherapy and autologous stem cell transplantation Prior autologous stem cell transplantation < month or allogenic stem cell transplantation < months prior to CD. Patients who have undergone a prior allogeneic or autologous stem cell transplantation within the previous six months Patients with pathologically diagnosed who have received induction chemotherapy, with or without autologous stem cell transplantation (AuSCT), and who have qualified to receive lenalidomide-based maintenance therapy for their multiple myeloma (MM) One or more prior allogeneic stem cell transplantation (prior autologous transplant is acceptable) Autologous stem cell transplantation less than days prior to study day Prior autologous stem cell transplantation < month or allogeneic stem cell transplantation < months prior to CD. Patients must not have had prior stem cell transplantation (autologous or allogeneic) Patients receiving autologous stem cell transplantation must wait weeks before initiation of study drug administration.