Inclusion Criteria:

          -  Documented informed consent of the participant and/or legally authorized
             representative

               -  Assent, when appropriate, will be obtained per institutional guidelines

          -  Be willing to provide archival tissue of a biopsy that was performed after the
             frontline systemic therapy

               -  If unavailable, exceptions may be granted with study principal investigator (PI)
                  approval

          -  Eastern Cooperative Oncology Group (ECOG) =< 2

          -  Histologically confirmed diagnosis of diffuse large B-cell lymphoma according to the
             World Health Organization (WHO) classification, with hematopathology review at the
             participating institution. Subtypes of DLBCL including transformed indolent lymphomas
             (TIL), primary mediastinal large B-cell lymphoma (PMBCL), and aggressive B-cell
             lymphoma unclassified (BCL-U) are eligible

          -  Biopsy-proven relapsed or refractory disease after 1 line of frontline CD20-directed
             immunotherapy with anthracycline- or anthracenedione-based multi-agent chemotherapy.
             Monotherapy with rituximab or other CD20-directed immunotherapy prior to frontline
             chemotherapy or as maintenance therapy, and radiation therapy in a limited field or as
             a part of the frontline treatment plan are permitted

          -  Prior lymphoma therapy should be completed at least 2 weeks before start of protocol
             therapy

          -  Measurable disease by computed tomography (CT) or positron emission tomography
             (PET)/CT scan with one or more sites of disease >= 1.5 cm in longest dimension

          -  Considered eligible for high-dose chemotherapy followed by ASCT

          -  Fully recovered from the acute toxic effects (except alopecia) to =< grade 1 to prior
             anti-cancer therapy

          -  Absolute neutrophil count (ANC) >= 1,000/mm^3 (without bone marrow involvement)

               -  NOTE: Growth factor is not permitted within 7 days of ANC assessment unless
                  cytopenia is secondary to disease involvement

          -  ANC >= 750/mm^3 (with bone marrow involvement)

               -  NOTE: Growth factor is not permitted within 7 days of ANC assessment unless
                  cytopenia is secondary to disease involvement

          -  Platelets >= 100,000/mm^3 (without bone marrow involvement)

               -  NOTE: Platelet transfusions are not permitted within 7 days of platelet
                  assessment unless cytopenia is secondary to disease involvement

          -  Platelets >= 75,000/mm^3 (with bone marrow involvement)

               -  NOTE: Platelet transfusions are not permitted within 7 days of platelet
                  assessment unless cytopenia is secondary to disease involvement

          -  Hemoglobin >= 8 g/dL (no erythropoietin and/or packed red blood cells (pRBC)
             transfusion allowed within 7 days prior to screening)

          -  Total bilirubin =< 1.5 X upper limit of normal (ULN). If hepatic involvement by
             lymphoma, or Gilbert's disease: =< 3 X ULN

          -  Aspartate aminotransferase (AST) =< 2.5 x ULN. If hepatic involvement by lymphoma: AST
             =< 5 x ULN

          -  Alanine aminotransferase (ALT) =< 2.5 x ULN. If hepatic involvement by lymphoma: ALT
             =< 5 x ULN

          -  Creatinine clearance of >= 50 mL/min per 24 hour urine test or the Cockcroft-Gault
             formula

          -  If not receiving anticoagulants: international normalized ratio (INR) OR prothrombin
             (prothrombin time [PT]) =< 1.5 x ULN. If on anticoagulant therapy: PT must be within
             therapeutic range of intended use of anticoagulants

          -  If not receiving anticoagulants: activated partial thromboplastin time (aPTT) =< 1.5 x
             ULN. If on anticoagulant therapy: aPTT must be within therapeutic range of intended
             use of anticoagulants

          -  Women of childbearing potential (WOCBP): negative urine or serum pregnancy test. If
             the urine test is positive or cannot be confirmed as negative, a serum pregnancy test
             will be required

          -  Agreement by females and males of childbearing potential* to use an effective method
             of birth control or abstain from heterosexual activity for the course of the study
             through at least 12 months after the last dose of polatuzumab vedotin or rituximab for
             women, at least 5 months following the last dose of polatuzumab vedotin or 3 months
             following the last dose of rituximab for men, and at least 6 months following the last
             dose of ifosfamide, carboplatin, or etoposide for both women and men

               -  Childbearing potential defined as not being surgically sterilized (men and women)
                  or have not been free from menses for > 1 year (women only)

        Exclusion Criteria:

          -  Patients who are not hematopoietic stem cell transplant candidates are excluded

          -  Prior solid organ transplantation

          -  Systemic steroid therapy or any other form of immunosuppressive therapy for lymphoma
             symptom control must be tapered down to =< 10 mg/day prednisone or equivalent.
             Exceptions are:

               -  Inhaled or topical steroids

               -  Adrenal replacement doses > 10 mg daily prednisone equivalents in the absence of
                  active autoimmune disease

          -  Peripheral neuropathy >= grade 2 or demyelinating form of Charcot-Marie-Tooth disease

          -  Known active central nervous system (CNS) involvement by lymphoma, including
             leptomeningeal involvement

          -  Active infection requiring systemic therapy

          -  Other active malignancy requiring therapy. Exceptions include basal cell carcinoma of
             the skin or squamous cell carcinoma of the skin that has undergone potentially
             curative therapy or in situ cervical cancer

          -  History of severe allergic reactions attributed to compounds of similar chemical or
             biologic composition to study agents

          -  Recent major surgery (within 4 weeks) prior to start of protocol therapy, other than
             for diagnosis

          -  Symptomatic cardiac disease (including symptomatic ventricular dysfunction,
             symptomatic coronary artery disease, and symptomatic arrhythmias), cerebrovascular
             event/stroke or myocardial infarction within the past 6 months

          -  Known active hepatitis B virus (HBV) or hepatitis C virus (HCV) infection. Patients
             with past HBV infection (defined as negative hepatitis B surface antigen [HBsAg] and
             positive hepatitis B core antibody [HBcAb]) are eligible if HBV DNA is undetectable.
             Patients who are positive for HCV antibody are eligible if polymerase chain reaction
             (PCR) is negative for HCV ribonucleic acid (RNA). Testing to be done only in patients
             suspected of having infections or exposures

          -  Known active human immunodeficiency virus (HIV) infection. Subjects who have an
             undetectable or unquantifiable HIV viral load with CD4 >= 200 and are on highly active
             antiretroviral therapy (HAART) medication are allowed. Testing to be done only in
             patients suspected of having infections or exposures

          -  History of or current progressive multifocal leukoencephalopathy (PML)

          -  Females only: Pregnant or breastfeeding

          -  Any other condition that would, in the investigator's judgment, contraindicate the
             patient's participation in the clinical study due to safety concerns with clinical
             study procedures

          -  Prospective participants who, in the opinion of the investigator, may not be able to
             comply with all study procedures (including compliance issues related to
             feasibility/logistics)