Evaluate Optimization of CRS Profile for Glofit Monotherapy and Glofit+GemOx in R/R Aggressive B-NHL

Inclusion Criteria: * Life expectancy \>= 12 weeks. * For participants in the Glofit-GemOx combination therapy cohort (Cohort A) and the glofitamab monotherapy cohort (Cohort B), participant with histologically confirmed diffuse large B-cell lymphoma, (de novo or transformed from a follicular lymphoma (FL); participants with transformed FL must be relapsed or refractory (R/R) to standard therapies of transformed FL) with one of the following diagnoses according to World Health Organization, fifth edition (Alaggio et al. 2022). A fresh biopsy at study entry is not mandated. The histology can be confirmed based on fresh biopsy, or pathology report from a previous biopsy or an assessment of archival tumor tissue. 1. Diffuse Large B-Cell Lymphoma (DLBCL) not otherwise specified (NOS). 2. High-Grade B-Cell Lymphoma (HGBL), NOS. 3. DLBCL/HGBL with myelocytomatosis proto-oncogene (MYC) and B-cell lymphoma 2 (BCL2) rearrangements. * R/R disease, defined as: relapsed = disease that has recurred following a response that lasted \>/= 6 months after completion of the last line of therapy; refractory = disease that did not respond to or that progressed \< 6 months after completion of the last line of therapy. * At least one line of prior systemic therapy. * Participants who have failed one prior line of therapy (eligible to Cohort A) must not be a candidate for high-dose chemotherapy followed by autologous stem cell transplant. * At least one bi-dimensionally measurable (\> 1.5 cm) nodal lesion, or one bi-dimensionally measurable (\> 1 cm) extranodal lesion, as measured on CT scan. * Eastern Cooperative Oncology Group (ECOG) status of 0, 1, or 2. * According to the investigator's judgment, participants should be able to receive the step-up dose regimen in an outpatient setting. Exclusion Criteria: * Prior enrollment in Studies GO41943 (NCT04313608), GO41944 (STARGLO; NCT04408638), or Study GO44900 (NCT06624085). * Participant has failed only one prior line of therapy and is a candidate for stem cell transplantation. * Any history of Waldenstrom's macroglobulinemia. * Primary mediastinal B-cell lymphoma. * History of severe allergic or anaphylactic reactions to humanized or murine monoclonal antibodies (or recombinant antibody-related fusion proteins) or known sensitivity or allergy to murine products. * Contraindication to obinutuzumab, gemcitabine or oxaliplatin, or tocilizumab. For participants in the monotherapy cohort (Cohort B), participants with contraindication to obinutuzumab or tocilizumab will be excluded. * Prior treatment with glofitamab or other bispecific antibodies targeting both CD20 and CD3. * For the Glofit-GemOx combination therapy cohort (Cohort A), prior treatment with gemcitabine or oxaliplatin. * For the Glofit-GemOx combination therapy cohort (Cohort A), peripheral neuropathy or paresthesia assessed to be Grade \>= 2 according to National Cancer Institute Common Terminology Criteria for Adverse Events (NCI CTCAE) v5.0 at enrolment. * Treatment with radiotherapy, chemotherapy, immunotherapy, immunosuppressive therapy, or any investigational agent for the purposes of treating cancer within 2 weeks prior to first study treatment. * Treatment with monoclonal antibodies for the purposes of treating cancer within 4 weeks prior to first study treatment. * Primary or secondary CNS lymphoma at the time of recruitment. * Prior CNS involvement that has been definitively treated and confirmed via magnetic resonance imaging (MRI) or cerebrospinal fluid analysis to be in complete remission is permissible. * Current or history of CNS disease, such as stroke, epilepsy, CNS vasculitis, or neurodegenerative disease. * History of other primary malignancy, with exceptions defined by the protocol. * Significant or extensive cardiovascular disease. * Significant pulmonary disease (including moderate or severe obstructive pulmonary disease). * Known active bacterial, viral, fungal, mycobacterial, parasitic, or other infection (excluding fungal infections of nail beds) at study enrollment or any major episode of infection (as evaluated by the investigator) within 4 weeks prior to the first study treatment. * Positive for: severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2); tuberculosis; hepatitis B virus (HBV); hepatitis C virus (HCV); chronic active Epstein-Barr viral infection. * Known or suspected history of hemophagocytic lymphohistiocytosis (HLH) or progressive multifocal leukoencephalopathy. * Adverse events from prior anti-cancer therapy that have not resolved to Grade 1 or better (with the exception of alopecia and anorexia). * Administration of a live, attenuated vaccine within 4 weeks before first study treatment administration or anticipation that such a live, attenuated vaccine will be required during the study. * Prior solid organ transplantation or prior allogenic stem cell transplant. * Active autoimmune disease requiring treatment. * Prior treatment with systemic immunosuppressive medications (including, but not limited to, cyclophosphamide, azathioprine, methotrexate, thalidomide, and antitumor necrosis factor agents), within 4 weeks prior to first dose of study treatment. * Ongoing systemic corticosteroid use which, in the opinion of the investigator, puts the participant at increased risk of steroid-related iatrogenic adrenal insufficiency. * Recent major surgery (within 4 weeks before the first study treatment) other than for diagnosis. * Clinically significant history of cirrhotic liver disease. * Any other diseases, metabolic dysfunction, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use of an investigational drug or that may affect the interpretation of the results or renders the participant at high-risk from treatment complications. * Pregnancy or breastfeeding, or intention of becoming pregnant during the study or within 18 months after the final dose of study treatment.