Grade b FL Part : A confirmed diagnosis of FL Grade , , or a, which has relapsed after, or been refractory to ? prior therapy for FL, or subjects who have not previously received systemic anticancer therapy for FL., and which requires treatment. Part :Histologically confirmed MZL including splenic, nodal, and extranodal sub- types Participantts with diffuse large B-cell lymphoma (DLBCL) relapsed or refractory to ? course of chemotherapy including an anti-CD monoclonal antibody, and not eligible for autologous stem cell transplantation (ASCT) (including due to chemorefractory disease). Participants with transformed FL are eligible, provided DLBCL histology is biopsy-confirmed prior to study entry and a treatment regimen as described above has been administered. The Sponsor retains the option to limit the number of participants enrolled with transformed FL. Grb-FL TH-FL Diagnosis of t-FL/DLBCL is allowed. However, other B-cell lymphomas including other transformed indolent lymphomas/DLBCL per the WHO classification, and Burkitt lymphoma are not eligible. histologically-confirmed relapsed or refractory CD+ B-cell lymphoma of one of the following types, with documented disease progression or recurrence following the immediate prior therapy: DLBCL (regardless of cell of origin or underlying molecular genetics), MCL, PMBCL, Grb-FL, TH-FL (prior dx of FL before transforming to DLBCL). Histologically proven diagnosis of grade , , or A FL The diagnosis of relapsed FL must have been made within the last months of screening if no other treatment is given for the FL in the interim; if an interim treatment is given within the last month, re-biopsy will be required even if there is already a biopsy proven relapsed FL within the last months Grade B FL or evidence of transformation of FL to a more aggressive lymphoma Histologically confirmed FL. Documented CD+ FL. Clinical evidence of transformation to a more aggressive subtype of lymphoma or Grade B FL. Patient with aggressive NHL must have received prior therapy at a minimum:\r\n* Anti-CD monoclonal antibody unless tumor is CD negative and\r\n* An anthracycline containing regimen\r\n* Transformed FL must have had therapy for FL and be refractory to chemotherapy for DLBCL PHASE II: Histologically confirmed B-cell NHL:\r\n* Cohort : with only de novo DLBCL,\r\n* Cohort : with only FL of grade , or a Part (Dose Escalation): Diagnosis of B-cell DLBCL, FL, MCL, or HL, as documented by medical records. Patients not previously treated for their FL, including any previous treatment for FL under clinical trials except localized radiation therapy for previous limited stage disease. For Part and Part of the study, participants with R/R FL, MZL/MALT, MCL, or any other NHL subtypes according to the WHO classification. Follicular lymphoma(FL) grade--a ) Transformed FL ) Small lymphocytic lymphoma ) Histological Grade b FL ) Subject will have undergone autologous transplant within weeks of planned leukapheresis or has undergone allogeneic transplant. ) Subject has evidence of involvement of the heart by lymphoma or requirement for urgent therapy due to ongoing or impending oncologic emergency (e.g. mass effect, tumor lysis syndrome, etc.) Histologically confirmed diagnosis of B-cell follicular lymphoma (FL), and grade limited to , , or a based on criteria established by the WHO classification of tumors of hematopoietic and lymphoid tissues History of histologically documented r/r Grades to a FL, or r/r DLBCL Histologically confirmed diagnosis of FL or MCL according to WHO For participants enrolled in the safety run-in phase: lymphoma classified as either relapsed or refractory FL after treatment with at least one prior chemoimmunotherapy regimen or previously untreated Grade , , or a FL that requires treatment Documented TI/A, FL, or VL mutations (if already available - not required for screening) Grade b FL Follicular lymphoma (FL) grade --a. Histologically confirmed diagnosis of FL grade b. Grade , , or a FL without pathologic evidence of transformation Grade B FL and/or clinical evidence of transformation to a more aggressive subtype of lymphoma. FL Follicular lymphoma (FL) grade --a Diagnosis Arm A: CLL (including SLL), DLBCL, or FL; SLL, DLBCL, and FL must be histologically confirmed Arm B: Histologically confirmed SLL or previous confirmation of B-cell CLL with a characteristic immunophenotype by flow cytometry Arm C: Histologically confirmed aggressive B-cell DLBCL, including FL transforming to DLBCL, transformed indolent lymphoma, MCL, or Grade b FL, according to the World Health Organization (WHO)/American Joint Committee on Cancer (AJCC) criteria Arm D: Histologically confirmed anti-CD-refractory (defined as any subject with less than a PR to any prior anti-CD-based therapy or progression within months after completing therapy with any anti-CD-based regimen, including maintenance rituximab) aggressive B-cell DLBCL, including FL transforming to DLBCL, transformed indolent lymphoma, MCL, or Grade b FL, according to the WHO/AJCC criteria Baseline PET or PET/CT scans must show positive lesions compatible with CT-defined anatomical tumor sites (only applicable for FL, DLBCL, MCL, transformed indolent lymphoma, and FL transforming to DLBCL) CLL (Arms A and B): Follicular lymphoma (FL) Grade , , or a Diagnosis of CD-positive FL: Transformation to a more aggressive subtype of lymphoma or grade b FL Grade b FL Histologically documented FL (Grade , and A) Not previously treated with prior anti-cancer therapy for FL FL with evidence of large cell transformation Any prior history of other hematologic malignancy besides FL or myelodysplasia Follicular lymphoma (FL) Participants must have histologically confirmed follicular lymphoma (FL) of Grade , , or a Participants must have received at least one prior therapy for FL Follicular Lymphoma (FL) must have at least lesion that can be biopsied at screening and on treatment Grade b FL Histologically confirmed aggressive B-cell DLBCL, including FL transforming to DLBCL & Grade III FL Patients undergoing their first T-cell replete allogenic (allo)-HCT for CLL, MCL, follicular lymphoma (FL), Hodgkin disease (HD) Progression of CLL or MCL or FL or HD at time of transplant Histologically confirmed aggressive B-cell DLBCL, including follicular lymphoma (FL) transforming to DLBCL For the expansion phase, participants must have histologically confirmed diagnosis of advanced DLBCL or follicular lymphoma FL.