Testing the Addition of an Immunotherapy Agent, Atezolizumab, When Given With the Usual Chemo-Immunotherapy Drug Combination (Rituximab Plus Gemcitabine and Oxaliplatin) for Relapsed/Refractory (That Has Come Back or Not Responded to Treatment) Transformed Diffuse Large B-Cell Lymphoma

Patients with prior allogeneic bone marrow transplantation or prior solid organ transplantation

Patients who have previously received gemcitabine plus oxaliplatin therapy

Patients who have had chemotherapy or radiotherapy within 2 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events (other than alopecia) due to agents administered more than 2 weeks earlier; however, the following therapies are allowed:

* Hormone-replacement therapy or oral contraceptives

* Herbal therapy \> 1 week prior to cycle 1, day 1 (herbal therapy intended as anticancer therapy must be discontinued at least 1 week prior to cycle 1, day 1)

Prior treatment with anti-PD-1, or anti-PD-L1 therapeutic antibody or pathway-targeting agents

* Patients who have received prior treatment with anti-CTLA-4 may be enrolled, provided the following requirements are met:

* Minimum of 12 weeks from the first dose of anti-CTLA-4 and \> 6 weeks from the last dose

* No history of severe immune-related adverse effects from anti-CTLA-4 (National Cancer Institute \[NCI\] Common Terminology Criteria for Adverse Events \[CTCAE\] version 5.0)

Treatment with any other investigational agent within 3 weeks prior to cycle 1, day 1

Treatment with systemic immunostimulatory agents (including, but not limited to, interferon \[IFN\]-alpha or interleukin \[IL\]-2) within 6 weeks prior to cycle 1, day 1

Treatment with systemic immunosuppressive medications (including, but not limited to, prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor \[anti-TNF\] agents) within 2 weeks prior to cycle 1, day 1

* Patients who have received acute, low dose, systemic immunosuppressant medications (e.g., a one-time dose of dexamethasone for nausea) may be enrolled

* The use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone) for patients with orthostatic hypotension or adrenocortical insufficiency is allowed

Patients taking bisphosphonate therapy for symptomatic hypercalcemia; use of bisphosphonate therapy for other reasons (e.g., bone metastasis or osteoporosis) is allowed

Patients requiring treatment with a RANKL inhibitor (e.g. denosumab) who cannot discontinue it before treatment with atezolizumab

Patients with known active central nervous system (CNS) involvement by lymphoma, including leptomeningeal involvement

Known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies

History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins

History of allergic reactions attributed to compounds of similar chemical or biologic composition to other agents used in study

Known clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver; and inherited liver disease

* Patients with past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen \[HBsAg\] test and a positive anti-HBc \[antibody to hepatitis B core antigen\] antibody test) are eligible

* Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA)

History or risk of autoimmune disease, including, but not limited to, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjogren's syndrome, Bell's palsy, Guillain-Barre syndrome, multiple sclerosis, autoimmune thyroid disease, vasculitis, or glomerulonephritis

* Patients with a history of autoimmune hypothyroidism on a stable dose of thyroid replacement hormone may be eligible

* Patients with controlled type 1 diabetes mellitus on a stable insulin regimen may be eligible

* Patients with eczema, psoriasis, lichen simplex chronicus of vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis would be excluded) are permitted provided that they meet the following conditions:

* Patients with psoriasis must have a baseline ophthalmologic exam to rule out ocular manifestations

* Rash must cover less than 10% of body surface area (BSA)

* Disease is well controlled at baseline and only requiring low potency topical steroids (e.g., hydrocortisone 2.5%, hydrocortisone butyrate 0.1%, fluocinolone 0.01%, desonide 0.05%, alclometasone dipropionate 0.05%)

* No acute exacerbations of underlying condition within the last 12 months (not requiring psoralen plus ultraviolet A radiation \[PUVA\], methotrexate, retinoids, biologic agents, oral calcineurin inhibitors; high potency or oral steroids)

History of idiopathic pulmonary fibrosis, pneumonitis (including drug induced), organizing pneumonia (i.e., bronchiolitis obliterans, cryptogenic organizing pneumonia, etc.), or evidence of active pneumonitis on screening chest computed tomography (CT) scan; history of radiation pneumonitis in the radiation field (fibrosis) is permitted

Patients with active tuberculosis (TB) are excluded

Severe infections within 4 weeks prior to cycle 1, day 1, including, but not limited to, hospitalization for complications of infection, bacteremia, or severe pneumonia

Signs or symptoms of infection within 2 weeks prior to cycle 1, day 1

Received oral or intravenous (IV) antibiotics within 2 weeks prior to cycle 1, day 1; patients receiving prophylactic antibiotics (e.g., for prevention of a urinary tract infection or chronic obstructive pulmonary disease) are eligible

Major surgical procedure within 28 days prior to cycle 1, day 1 or anticipation of need for a major surgical procedure during the course of the study

Administration of a live, attenuated vaccine within 4 weeks before cycle 1, day 1 or anticipation that such a live, attenuated vaccine will be required during the study and up to 5 months after the last dose of atezolizumab

* Influenza vaccination should be given during influenza season only (approximately October to March); patients must not receive live, attenuated influenza vaccine within 4 weeks prior to cycle 1, day 1 or at any time during the study

Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements

Pregnant women are excluded from this study because atezolizumab, gemcitabine, and oxaliplatin are agents with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with atezolizumab, gemcitabine, and oxaliplatin, breastfeeding should be discontinued if the mother is treated with atezolizumab, gemcitabine, and oxaliplatin; these potential risks may also apply to other agents used in this study

What this study is about