Inclusion Criteria:

1. Age 65-79 years with a fitness assessment of unfit or frail per simplified GA (Appendix 1, www.filinf.it/epi)
2. Age ≥80 years with any fitness level
3. Pathologically confirmed DLBCL, HGBCL or transformed lymphoma
4. No prior systemic anti-lymphoma therapy (prednisone/equivalent up to 100 mg daily x 7 days is permissible)
5. Ann Arbor Stage 2 bulky, 3 or 4 disease (Appendix 1)
6. Any IPI score (Appendix 1)
7. Anthracycline eligible: LVEF ≥ 45% by echocardiogram or MUGA scan.
8. Must have at least one bi-dimensionally measurable lesion (\>1.5 cm in its largest dimension for nodal lesions, or \>1.0 cm in its largest dimension for extranodal lesions by computerized tomography \[CT\] scan or MRI)
9. Eastern Cooperative Oncology Group performance status ≤ 2 (Appendix 1)
10. Must have adequate organ and marrow status:

1. Absolute neutrophil count (ANC) ≥1,000/mm3 or ≥500/mm3 if due to disease involvement in the bone marrow
2. Platelet count ≥50,000 cells/mm3 or ≥25,000/mm3 if due to disease involvement in the bone marrow
3. Patients who do not meet criteria for bone marrow function due to marrow involvement of lymphoma and/or other disease-related cytopenias (e.g., immune thrombocytopenia) may be enrolled into the study after discussion with, and confirmation by the PI.
4. Serum creatinine ≤ULN OR estimated Creatinine Clearance (CrCl) ≥30 mL/min (Cockcroft-Gault formula or other institutional standard methods)
5. Serum aspartate transaminase (AST) or alanine transaminase (ALT) ≤3 x upper limit of normal (ULN)
6. Total bilirubin ≤ 1.5 x ULN (≤3 if due to Gilbert's syndrome or liver involvement by the lymphoma
7. Patients who do not meet criteria for liver function due to liver involvement of lymphoma may be enrolled into the study after discussion with, and confirmation by the PI.
11. Negative HIV test at screening, with the following exception: Individuals with a positive HIV test at screening are eligible provided, prior to enrollment, they are stable on antiretroviral therapy, have a CD4 count ≥200/µL, and have an undetectable viral load.
12. Signed Informed Consent Form(s)
13. Ability to comply with all the study-related procedures, in the investigator's judgement
14. Female patients who are not of child bearing potential (i.e., who are postmenopausal or surgically sterile). For male participants: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods, and agree to refrain from donating sperm, as defined below: With a female partner of childbearing potential or pregnant female partners, male participants must remain abstinent or use a condom plus an additional contraceptive method that together result in a failure rate of \< 1% per year during the treatment period and for at least 6 months after pretreatment with obinutuzumab, 6 months after the last dose of polatuzumab, 160 days after the last dose of rituximab, 2 months after the final dose of glofitamab or 2 months after the last dose of tocilizumab (as applicable), whichever is longer. Male participants must refrain from donating sperm during this same period. The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the individual. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not adequate methods of contraception. If required per local guidelines or regulations, locally recognized adequate methods of contraception and information about the reliability of abstinence will be described in the local Informed Consent Form.

Exclusion Criteria:

1. Prior systemic anti-lymphoma therapy (localized radiation, steroids and antibiotics are permitted)
2. Prior solid organ transplantation
3. Prior allogeneic stem cell transplantation
4. Active CNS involvement
5. Uncontrolled HIV or active HBV or HCV infection (controlled HIV with undetectable viral load and previously treated HBV and HCV are allowed) 5.1 Participants with occult or prior hepatitis B infection (defined as positive total hepatitis B core antibody and negative HBsAg) may be included if hepatitis B virus (HBV) DNA is undetectable at the time of screening. Such participants must be willing to undergo HBV DNA testing on Day 1 of every cycle and every 3 months for at least 12 months after the final cycle of study treatment and appropriate antiviral therapy as indicated.

5.2 Participants positive for HCV antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV RNA
6. Uncontrolled active systemic infection
7. Major surgery within 4 weeks of the first dose of study drug (exceptions may be allowed after discussion with PI if patient has fully recovered from procedure and antilymphoma therapy is urgently needed)
8. Significant or extensive history of cardiovascular disease such as New York Heart Association Class III or IV cardiac disease or Objective Assessment Class C or D, myocardial infarction within the last 3 months prior to the start of Cycle 1, unstable arrhythmias, or unstable angina.
9. Uncontrolled autoimmune disorder
10. A history of confirmed progressive multifocal leukoencephalopathy
11. Any life-threatening illness, medical condition, or organ system dysfunction that, in the investigator's opinion, could compromise the subject's safety or risk study outcomes
12. Inability to comply with all the study-related procedures, in the investigator's judgement.
13. Contraindication to any of the individual components of polatuzumab, R-miniCHP and glofitamab or history of severe allergic or anaphylactic reactions to humanized or murine monoclonal antibodies or known sensitivity or allergy to murine products
14. Prior treatment with systemic immunotherapeutic agents, including but not limited to, radio-immuno-conjugates, antibody-drug conjugates, immune/cytokines and monoclonal antibodies (mAbs) (e.g., anti-cytotoxic T lymphocyte associated protein 4, anti-PD-1, and anti-PD-L1) within 4 weeks or five half-lives of the drug, whichever is shorter 15. Prior use of any monoclonal antibody for the purposes of treating cancer within 3 months of the start of Cycle 1
15. Prior use of any monoclonal antibody for the purposes of treating cancer within 3 months of the start of Cycle 1
16. Any investigational therapy for the purposes of treating cancer within 28 days prior to the start of Cycle 1
17. Prior radiotherapy to the mediastinal/pericardial region. Radiotherapy to non-target lesion sites will be permitted.
18. Corticosteroid use \> 50 mg/day of prednisone or equivalent, for purposes other than lymphoma symptom control 18.1 Participants receiving corticosteroid treatment with ≤ 50 mg/day of prednisone or equivalent for reasons other than lymphoma symptom control (e.g., rheumatoid arthritis) must be documented to be on a stable dose of at least 4 weeks duration prior to the start of cycle 18.2 Corticosteroid therapy for control of cancer symptoms or side effects of prior treatment (e.g., nausea or B-symptoms) is permitted.

18.3 The use of inhaled corticosteroids is permitted. 18.4 The use of mineralocorticoids for management of orthostatic hypotension is permitted.

18.5 The use of physiologic doses of corticosteroids for management of adrenal insufficiency is permitted.
19. Participants who require lymphoma symptom control during screening may receive steroids in the following manner: - Up to 100 mg of prednisone PO (or equivalent steroids) per day for up to 7 days are allowed. Prednisone dose is at the discretion of the treating physician, provided that the dose is within the above specified dosage range. - As part of the pre-phase treatment, vincristine or rituximab may not be administered.
20. History of other malignancy that could affect compliance with the protocol or interpretation of results:

20.1 Participants with a history of curatively treated basal or squamous cell carcinoma or melanoma of the skin or in situ carcinoma of the cervix at any time prior to the study are eligible.

20.2 Participants with any malignancy appropriately treated with curative intent and the malignancy has been in remission without treatment for ≥ 2 years prior to enrollment are eligible.

20.3 Participants with low-grade, early-stage prostate cancer (Gleason score 6 or below, Stage 1 or 2) with no requirement for therapy at any time prior to study are eligible.

20.4 Patients with other concomitant malignancies may be eligible after discussion with, and confirmation by the PI
21. Live, attenuated vaccine within 4 weeks before study treatment infusion on Day 1 of Cycle 1 or anticipation that such a live, attenuated vaccine will be required during the study. Live vaccines during the study and until participants B cells recover, are prohibited.

21.1 Influenza vaccination should be given during influenza season only. Participants must not receive live, attenuated influenza vaccine at any time during the study treatment period.