Inclusion Criteria:  The informed consent form must be signed before any study specific tests or procedures are done Adult male and female patients ≥18 years (≥16 years in the UK*) at the time of inclusion in the study (* In the UK an "adult" means a person who has attained the age of 16 years, according to The Medicines for Human Use (Clinical Trials) Regulations 2004, Part 1 Point 2.) Ability to understand and follow study-related instructions  Risk group: All patients with one of the following histologically defined entities: Histological diagnosis of primary refractory or relapsed aggressive B-cell non-Hodgkin lymphoma (B-NHL), confirmed by a biopsy of involved nodal or extranodal site. Patients with any of the following histologies can be included:  DLBCL not otherwise specified (NOS) T-cell/histiocyte-rich large B-cell lymphoma Primary cutaneous DLBCL, leg type Epstein-Barr virus (EBV)-positive DLBCL, NOS DLBCL associated with chronic inflammation Primary mediastinal (thymic) large B-cell lymphoma High-grade B-cell lymphoma, with MYC and BCL2 and/or BCL6 rearrangements High-grade B-cell lymphoma, NOS  Refractory disease is defined as no complete remission to first line therapy; subjects who are intolerant to first line therapy are excluded. Three groups of patients are eligible:  Progressive disease (PD) as best response to first line therapy (biopsy not mandatory if diagnostic sample available). Stable disease (SD) as best response after at least 4 cycles of first line therapy (e.g., 4 cycles of R-CHOP) (biopsy not mandatory if diagnostic sample available). Partial response (PR) as best response after at least 6 cycles, and biopsy-proven residual disease or disease Progression after the partial response.  Relapsed disease is defined as complete remission to first line therapy followed by biopsy proven disease relapse.  Performance Status ECOG 0-2 at time of randomization or ECOG 3 at screening if this is DLBCL-related and has improved to ECOG 2 or less with a 7-day steroid treatment during the screening Phase (e.g. 1 mg/kg prednisone). Information on all 5 International Prognostic Index (IPI) factors Staging (PET-CT based-staging according to Lugano criteria 2014). Patients must have PET-positive lesions. Subjects must have received adequate first line therapy including at a minimum: i) anti-CD20 monoclonal antibody unless Investigator determines that tumor is CD20 negative, and ii) an anthracycline containing chemotherapy Regimen Intent to proceed to high-dose therapy (HDT) and stem cell transplantation (SCT) if response to second line therapy Adequate hematological function, as defined by: hemoglobin ≥ 8 g/dL, absolute neutrophil count (ANC) ≥ 1.0 x 109/L OR ≥ 0.5 x 109/L if neutropenia is attributable to underlying disease and before the administration of steroids, and platelet count ≥ 75 x 109/L OR ≥ 50 x 109/L if thrombocytopenia is attributable to Underlying disease Women of childbearing potential must have a negative pregnancy test result within 7 days prior to the first study drug Administration For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures, and agreement to refrain from donating eggs For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures, and agreement to refrain from donating sperm  Exclusion Criteria:  (1) Serious accompanying disorder leading to impaired organ function causing significant clinical problems and reduced life expectancy of less than 3 months. In particular, patients with the following organ dysfunction caused by accompanying disorders are to be excluded:  Heart failure with left ventricular ejection fraction (LVEF) < 45% Impaired pulmonary function with vital capacity (VC) or forced expiratory volume (FEV1) < 50% of normal (only in case of history of significant pulmonary disease) Impaired renal function with glomerular filtration rate (GFR) < 50 mL/min (calculated) Impaired liver function with alanine aminotransferase (ALAT), aspartate aminotransferase (ASAT) or Bilirubin > 1.5 x upper limit of normal (ULN). If elevation is caused by the disease, threshold of 2.5 x ULN is accepted  Peripheral neuropathy > Grade II (2) Human immunodeficiency virus (HIV)-positivity with detectable viral load and/or a CD4+ count below 0.3/nL  (3) Hepatitis B and C as defined by seropositivity (HBsAG and anti HBe/ anti HBc; anti-Hc); in case of false positive serology (transfused antibodies) negative PCR-results will allow patient inclusion. Patients with occult or prior HBV infection (defined as negative HBsAg and positive hepatitis B core antibody [HBcAb]) may be included if HBV DNA is undetectable, provided that they are willing to undergo DNA testing on Day 1 of every cycle and monthly for at least 12 months after the last cycle of study Treatment  (4) Known active bacterial, viral, fungal, mycobacterial, parasitic, or other infection (excluding fungal infections of nail beds) at study inclusion or any unresolved major episode of infection (as evaluated by the investigator) within 1 week prior to Cycle 1 Day 1  (5) Patients with suspected or latent tuberculosis. Latent tuberculosis needs to be confirmed by positive interferon-gamma release Assay  (6) Primary or secondary central nervous system (CNS) lymphoma at the time of recruitment  (7) Richter's transformation or prior chronic lymphocytic leukemia (CLL)  (8) Vaccination with a live vaccine within 4 weeks prior to Treatment  (9) Recent major surgery (within 6 weeks before the start of Cycle 1 Day 1) other than for diagnosis  (10) Treatment with radiotherapy, chemotherapy, immunotherapy, immunosuppressive therapy, or any investigational agent for the purposes of treating cancer within 2 weeks prior to Cycle 1 Day 1  (11) Received more than one line of therapy for DLBCL  (12) Received polatuzumab vedotin as part of the first line therapy  (13) 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 render the patient at high risk from treatment complications  (14) Ongoing treatment or study procedures within any other Investigational Medicinal Product (IMP) clinical trial with the exception of follow-up. In case of a preceding clinical trial, last application of the respective IMP(s) must have been done more than five elimination half-lives before start of study medication in this trial.  (15) History of severe allergic or anaphylactic reactions to human, humanized, chimeric, or murine monoclonal antibodies  (16) History of hypersensitivity to any of the study drugs or their ingredients or to drugs with similar structure  (17) Contraindications according to the Investigator´s Brochure (IB) of polatuzumab vedotin or the local Summary of Product Characteristics (SmPCs) of the used rituximab, ifosfamide, carboplatin or etoposide products  (18) Criteria which in the opinion of the investigator preclude participation for scientific reasons, for reasons of compliance, or for reasons of the subject's Safety  (19) Pregnancy or breastfeeding, or intending to become pregnant during the study or within 12 months after the last dose of study drug  (20) Close affiliation with the investigator (e.g. a close relative) or persons working at the study site  (21) Subject is an employee of the sponsor or involved Contract Research Organization  At study inclusion, any organ impairment due to lymphoma infiltration is NOT regarded as an exclusion criterion.