Must not have received therapy with anti-CD monoclonal antibodies within  days of entry onto this study
DISEASE CHARACTERISTICS:\n\n          -  Histologically confirmed diagnosis of iNHL (Follicular lymphoma grade , , a;\n             marginal zone lymphoma; small lymphocytic lymphoma or lymphoplasmacytic lymphoma)\n             after treatment with at least  or more prior rituximab-containing regimens.\n\n               -  Anti-CD mAb-refractory disease is defined as progressive disease while on\n                  rituximab (or another treatment of an anti-CD monoclonal antibody) or\n                  progression within  months of rituximab-containing (or another treatment of an\n                  anti-CD antibody-containing) therapy.\n\n               -  Anti-CD mAb-sensitive disease is defined by a response to a prior\n                  rituximab-containing (or another treatment of an anti-CD monoclonal antibody)\n                  regimen, and relapse more than  months from the last administration of\n                  rituximab-containing (or another treatment of an anti-CD antibody-containing)\n                  therapy.\n\n          -  Measurable disease:\n\n               -  At least one lymph node group ? . cm in longest transverse dimension. Patients\n                  with cutaneous only disease may be enrolled if they have a clearly measurable\n                  skin lesion.\n\n               -  Relapsed or Refractory iNHL that has progressed during or following  or more\n                  prior systemic rituximab-containing (or another treatment of an anti-CD\n                  antibody-containing) regimens for lymphoma\n\n        PRIOR/CONCURRENT THERAPY:\n\n          -  No anti-lymphoma treatments within  days before the start of study treatment.\n\n          -  Must have recovered from side effects of prior treatments.\n\n        PATIENT CHARACTERISTICS:\n\n        Performance Status\n\n         ECOG , , or \n\n        Renal Function  Glomerular Filtration Rate (GFR) > mL/min or Serum creatinine ? . X\n        ULN\n\n        Bone Marrow Reserve\n\n          -  Platelets ?,/uL\n\n          -  Hemoglobin ? g/dL\n\n          -  Absolute Lymphocytes ?/uL\n\n          -  ANC/AGC ?/uL\n\n        Hepatic Function\n\n          -  Total bilirubin ? . X ULN (unless Gilbert's Syndrome or disease infiltration of\n             liver is present)\n\n          -  AST, ALT ? . X ULN, or ? . X ULN (if liver lymphoma is present)\n\n          -  No positive Hep C serology or active Hep B infection\n\n        Cardiovascular\n\n          -  No congestive heart failure <  months\n\n          -  No unstable angina pectoris <  months\n\n          -  No myocardial infarction <  months\n\n          -  No history of ventricular arrhythmias or severe cardiac dysfunction\n\n          -  No history of uncontrollable supraventricular arrhythmias\n\n          -  No NYHA Class > II CHF\n\n          -  No marked baseline prolongation of QT/QTc interval\n\n        Pulmonary\n\n         Normal clinical assessment of pulmonary function\n\n        Other\n\n          -  Negative serum pregnancy test if female and of childbearing potential\n\n          -  Women who are not pregnant or nursing\n\n          -  Subjects, both females and males, with reproductive potential must agree to use\n             effective contraceptive measures for the duration of the study\n\n          -  No known autoimmune disease other than corrected hypothyroidism\n\n          -  No known prior organ allograft or allogeneic transplantation\n\n          -  Not HIV positive\n\n          -  No active CNS involvement with lymphoma\n\n          -  No psychiatric illness/social situation that would limit compliance\n\n          -  No other illness that in the opinion of the investigator would exclude the subject\n             from participating in the study\n\n          -  Must provide informed consent and HIPPA authorization and agree to comply with all\n             protocol-specified procedures and follow-up evaluations\n\n          -  No active systemic infection requiring parenteral antibiotic therapy\n\n          -  No disease requiring systemic immunosuppressive therapy (inhaled or topical steroids\n             are allowed). Adrenal replacement steroid doses ?  mg daily prednisone equivalent\n             are permitted in the absence of active autoimmune disease.\n\n          -  No known histologic transformation from iNHL to DLBCL
Prior treatment with an anti-CD-directed agent
Patients must not have received prior treatment with inotuzumab ozogamicin; previous treatment with other anti-CD antibodies must have been completed at least  days prior to registration
Prior treatment with a monoclonal antibody or chimeric antigen receptor T cell (CAR-T) infusion for the treatment of AML (CD or other target).
Any systemic anti-cancer therapy within  weeks prior to CD of study therapy, with the following exception:\r\n* Any prior investigational anti-cancer therapy and/or monoclonal antibody is not permitted within  weeks of CD
B-cell lymphoma classified as either of the following: R/R FL after treatment with at least one prior chemoimmunotherapy regimen that included an anti-cluster of differentiation  (CD) monoclonal antibody; R/R 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 chemotherapy and autologous stem-cell transplantation, have failed second line combination chemotherapy, or experienced disease progression following autologous stem-cell transplantation
Prior treatment with CD or signal regulatory protein alpha (SIRP?) targeting agents.
Previous treatment with any anti-CD directed therapy
For obinutuzumab in combination with polatuzumab vedotin and lenalidomide (G + Pola + Len) treatment group: R/R FL after treatment with at least one prior chemoimmunotherapy regimen that included an anti-CD monoclonal antibody and for which no other more appropriate treatment option exists as determined by the investigator
For lymphoma patients only: At least one prior systemic chemotherapy including an alkylating agent and anthracycline (unless contraindicated), and an anti-CD monoclonal antibody if the tumor is CD+; prior treatment with anthracycline and alkylating agent is not required for patients with natural killer (NK)/T cell lymphoma but prior treatment with platinum based chemotherapy and/or l-asparaginase is required
Subjects who have undergone prior anti-CD or anti-CD CAR therapy will be eligible if < % of circulating levels of CD+ cells express the previous CAR by flow cytometry
Prior treatment with a CD or signal regulatory protein (SIRP) alpha targeting agent.
Part E only: Patients with biopsy-proven DLBCL who are intolerant to, or have disease that is relapsed/refractory after, at least two prior therapies, including any anti-CD monoclonal antibody and chemotherapy with curative intent
Prior anti-CD-directed therapies
Must have received adequate prior therapy for the underlying CD+ B-cell lymphoma, defined as an anti-CD mAb in combination with an anthracycline-containing chemotherapy regimen (i.e. chemo-immunotherapy) and at least one of the following:
Histologically documented cluster of differentiation (CD) -positive B-cell lymphoma classified as relapsed or refractory FL or DLBCL after treatment with at least two prior chemoimmunotherapy regimens that included an anti-CD monoclonal antibody (mAb) and for which no other more appropriate treatment option exists
Prior treatment with CD targeting therapy
Prior exposure to investigational immunotherapies, including anti-CTLA, anti-OX, anti-CD, anti-CD, anti-TNFR antibodies or other investigational immunotherapies, is acceptable
Prior CD directed therapy other than blinatumomab
Prior treatment with blinatumomab or CD-directed CAR T-cell therapy
Prior treatment\r\n* With any prior anti-CD/anti-CD CAR-T or cellular therapy (prior blinatumomab therapy is allowed)\r\n* Treatment with any prior gene therapy\r\n* Prior allogeneic hematopoietic stem cell transplant\r\n* Received chemotherapy, radiation or surgical resection of malignancy within  weeks prior to the start of lymphodepleting chemotherapy (day - to -)
Prior therapy with anti-CD or ISA.
Subjects who have undergone prior anti-CD or anti-CD CAR therapy will be eligible if < % of circulating levels of CD+ cells express the previous CAR by flow cytometry
Prior therapy for lymphoma including chemotherapy or immunotherapy including ibrutinib/anti-CD agents; patient may have received corticosteroids, but should be off them  weeks prior to study entry; known prior significant hypersensitivity to obinutuzumab (not including infusion reactions) or ibrutinib
must have received adequate prior therapy for the underlying CD+ B-cell lymphoma, defined as an anti-CD mAb in combination with an anthracycline-containing chemotherapy regimen (i.e. chemo-immunotherapy) and at least one of the following:
Prior treatment with any CD-directed therapy (e.g. blinatumomab, CD-directed chimeric antigen receptor T-cell therapy, anti-CD antibodies)
Prior treatment with any therapy that is targeted to B cell maturation antigen (BCMA) or any other CD-redirecting drug
CRITERIA FOR SCREENING: For patients in stage  only, prior treatment with any CD CAR T-cell therapy is excluded
Anti-CD monoclonal antibody unless investigator determines that tumor is CD negative, and
History of anti-CD or CAR-T therapy or history of prior randomization in ZUMA-
Prior treatment with cytotoxic drugs within  years of screening for any condition (example [e.g.], cancer, rheumatoid arthritis) or prior use of any anti-CD antibody
Receipt of >/= prior lines of therapy and progressed on treatment with an anti-CD monoclonal antibody and are refractory to both a PI and IMiD (Cohort D)
Responded to initial therapy for ?  year and relapsed after  or more lines of therapy, including an anti-CD monoclonal antibody
Prior treatment with any CD CAR T-cell therapy
Participants must have received at least one but no more than six prior treatment regimens. Prior treatment with an anti-CD agent, either alone or in combination, is allowed.
Participants who have received prior therapy with other anti-CD-targeting therapy.
Patients treatment history may not include anti-CD monoclonal antibody therapy (e.g., SGN-CD or Mylotarg)
Any major surgery, radiotherapy, cytotoxic chemotherapy, biologic therapy, immunotherapy, immunomodulatory drugs, experimental therapy within  weeks prior to the first dose of the study drugs; Note: prior therapy with anti cluster of differentiation (CD) monoclonal antibody, anti CD monoclonal antibody, and lenalidomide are allowed; for oral targeted therapies (such as idelalisib, venetoclax), a washout of  days is allowed
Any systemic anti-cancer therapy within  weeks prior to course  day  (CD) of study therapy\r\n* Exception is made for patients with EGFR or ALK re-arrangements who must have stopped TKI therapy at least  days prior to CD
Previous treatment with any anti-CD directed therapy
Patients having received anti-CD therapy ?  weeks prior to the first study dose.
Patients having received alemtuzumab (anti-CD) therapy ?  months prior to the first study dose.
Prior Therapy: therapy with monoclonal antibodies and/or chemotherapy must be stopped at least  days prior to anti-CD CAR-transduced T cell infusion, and recovery of treatment-associated toxicity to =< grade  is required prior to infusion of cells; for patients that have received prior DCI, the last dose must be at least  days prior to anti- CD CAR-transduced T cell administration; note that patients can be enrolled on this study at any time after or during therapy, but at least  days must elapse from the time of prior monoclonal antibody administration or chemotherapy until anti-CD CAR-transduced T cells are infused, and at least  days must elapse from the time of withdraw of immunosuppression, or DCI, or other immunomodulatory therapies such as lenalidomide until anti-CD CAR-transduced T cells are infused; systemic immunosuppression must be stopped at least  days prior to protocol entry; there is no time restriction in regard to prior intrathecal chemotherapy provided there is complete recovery from any acute toxic effects of such
 Prior anti-CD-directed therapies.
Anti-CD therapy within  weeks of enrollment;
Patients that who have relapsed after at least  prior anti-lymphoma therapy that include anti-CD monoclonal antibody and an alkylator chemotherapy agent, or at least  prior anti-lymphoma therapies that include anti-CD monoclonal antibody, may be included.
Anti-CD mAb-naive or anti CD mAb-sensitive (defined as progression of FL >=  months following prior anti-CD mAb containing therapy).
Prior treatment: Treated with two or more lines of prior therapy, with disease refractory to both a proteasome inhibitor and an immunomodulatory agent, and disease progression (as defined by International Myeloma Working Group (IMWG) criteria) following treatment with an anti-CD monoclonal antibody given as monotherapy or in combination therapy. The most recent treatment regimen must have contained an anti-CD monoclonal antibody.
Prior treatment with CD or signal regulatory protein alpha (SIRP?) targeting agents
Prior treatment with a CDxCD bispecific agent, T cells expressing CD specific chimeric antigen receptor, or toxin-conjugated to CD antibodies; prior treatment with naked anti-CD monoclonal antibody is permitted
Patients with a known hypersensitivity to gemtuzumab ozogamicin or its parts: recombinant humanized anti-CD monoclonal (hP.) antibody, calicheamicin derivatives or other ingredients
Treatment with any prior anti-CD/anti-CD therapy, or any other anti-CD therapy
Prior treatment with any prior anti-CD/anti-CD therapy, or any other anti-CD therapy
Has had treatment with any prior anti-CD/anti-CD therapy, or any other anti-CD therapy
Prior anti-CD therapies
Relapsed or refractory FL after treatment with at least one prior chemoimmunotherapy regimen that included an anti-CD monoclonal antibody and for which no other more appropriate treatment option exists as determined by the investigator
Anti-CD monoclonal antibody therapy within the last  months, or absence of circulating B cells
Prior CD directed therapy, including CAR+ T cell, BiTE, and antibody drug conjugate (ADC), with the exception of subjects who received KTE-C in this study and are eligible for re-treatment
For obinutuzumab + Atezo + Pola treatment group: relapsed or refractory FL after treatment with at least one prior chemoimmunotherapy regimen that included an anti-Cluster of Differentiation (CD) monoclonal antibody and for which no other more appropriate treatment option exists as determined by the investigator
Any major surgery, radiotherapy, chemotherapy, biologic therapy, immunotherapy, experimental therapy within  weeks prior to the first dose of the study drugs; for oral targeted therapies (such as ibrutinib, idelalisib, venetoclax), a washout of  days is allowed; Note: prior treatment with anti cluster of differentiation (CD) monoclonal antibody, anti CD monoclonal antibody and lenalidomide are allowed; prior treatment with anti-cytotoxic T-lymphocyte-associated protein  (CTLA-) and anti-programmed cell death  (PD) therapies is allowed after a wash-out of  half-lives
For cohort : Male or female subjects with histologic proof of follicular lymphoma grade , , or a relapsing after at least two prior systemic therapies, one of which must include rituximab (or other monoclonal CD antibody) or histologic proof of DLBCL relapsing after at least two prior systemic therapies, one of which must include rituximab (or other monoclonal CD antibody) and are considered ineligible for high dose therapy/autologous stem cell transplant
At least  prior treatment with a CD antibody combination chemo-immunotherapy regimen
Have documented CD+ B-cell malignancy, with active disease not responsive to prior therapy, for whom no standard of care options exists, and for whom treatment with an anti-CD antibody may be appropriate:
Anti-CD monoclonal antibodies within  days prior to leukapheresis
Subjects previously treated with anti-CD antibody or alemtuzumab are eligible provided their CD+ cell counts are ? /mm
Prior treatment with anti-cluster of differentiation (CD) monoclonal antibody or alemtuzumab within  months prior to start of therapy
Prior treatment with anti-cluster of differentiation (CD) monoclonal antibody or alemtuzumab within  months prior to start of therapy
Prior treatment with anti-CD monoclonal antibody or alemtuzumab within  weeks prior to start of therapy
Treatment with anti-CD monoclonal antibody within  months of randomization
Prior use of any monoclonal antibody (other than anti-CD) within  months prior to the start of Cycle , prior treatment with obinutuzumab was not allowed
Arm D: Refractory to ?  regimen containing any anti-CD-based therapy, including salvage regimens and maintenance rituximab. Refractory subjects are defined as any subject with less than a PR to any prior anti-CD-based therapies or progressed within  months after completing therapy with any anti-CD-based regimens, including maintenance rituximab. These subjects must not be eligible for hematopoietic SCT or BM transplant
Received anti-tumor therapy (chemotherapy, investigational product, radiotherapy, retinoid therapy, or hormonal therapy) within  weeks (less than  days) prior to CD with no residual toxicity >Grade ; antibody therapy, molecular targeted therapy within  half-lives prior to CD
Prior treatment with CAT- (BL), moxetumomab pasudotox (CAT-, HA), any pseudomonas-exotoxin-containing compound, or any anti-CD directed therapy at any time in the past
Use of any anti-cancer drug therapy within  days prior to Baseline (within  days for monoclonal antibodies [eg anti-CD]).
For obinutuzumab + polatuzumab vedotin + venetoclax treatment group, relapsed or refractory FL after treatment with at least one prior chemoimmunotherapy regimen that included an anti-cluster of differentiation  (CD) (anti-CD) monoclonal antibody (mAb) and for which no other more appropriate treatment option exists, as determined by the investigator
For rituximab + polatuzumab vedotin + venetoclax treatment group, relapsed or refractory DLBCL after treatment with at least one prior chemoimmunotherapy regimen that included an anti-CD mAb and for which no curative option exists as determined by the investigator
Prior treatment with tumor necrosis factor receptor superfamily agonists including OX, CD, CD (-BB), CD (GITR). One cohort also excludes anti CTLA-, anti PDL- and anti PDL-.
anti-CD monoclonal antibody unless investigator determines that tumor is CD-negative and
Prior treatment with anti-CD directed therapy unless CD expression is confirmed on tumor tissue obtained after the treatment
Washout from any prior investigational therapy of at least five times the T/ prior to CD
Washout of at least  weeks from the most recent radiation treatment prior to CD
Previous treatment with any anti-CD directed therapy
Prior use of monoclonal antibody (other than anti CD) within  months prior to randomization. Chemotherapy or other systemic lymphoma therapy within  weeks of study entry.
Previous anti-CD radioimmunotherapy (RIT) or non-rituximab anti-CD therapy (such as obinutuzumab) within  months prior to randomization. Patients who have received previous anti-CD RIT or non-rituximab anti-CD therapy (such as obinutuzumab) must have attained a partial or complete response lasting at least  months, and must have recovered from any hematologic or other toxicity.
Previous anti-lymphoma monoclonal antibody therapy (excluding anti-CD therapy and anti-CD RIT), chemotherapy, glucocorticoid, or other systemic therapy for lymphoma within  months prior to randomization.
Received prior treatment with a standard anthracycline and therapeutic anti-CD monoclonal antibody-based regimen;
Any major surgery, radiotherapy, chemotherapy, biologic therapy, immunotherapy, experimental therapy within  weeks prior to the first dose of the study drugs; for oral targeted therapies (such as ibrutinib, idelalisib, venetoclax), a washout of  days is allowed; Note: prior treatment with anti-cluster of differentiation (CD) monoclonal antibody, anti-CD monoclonal antibody and lenalidomide are allowed; prior treatment with anti-cytotoxic T-lymphocyte-associated protein  (CTLA-) and anti-programmed cell death (PD) therapies is allowed after a wash-out of  half-lives
All patients who have received anti-CD directed CART therapy and completed or discontinued early from a Novartis sponsored treatment protocol that utilized CD-directed CART cells or from any CD CART trial sponsored by the University of Pennsylvania with which Novartis has a contractual agreement to co-develop the CAR technology.
anti-CD monoclonal antibody unless investigator determines that tumor is CD-negative and
Prior CD targeted therapy