The target study population of this Phase 1b/3 registrational study is patients with R/R DLBCL who have completed at least 2 (but not more than 4) lines of prior rituximab-containing multi-agent chemotherapy, and/or in whom autologous stem cell transplant (ASCT) has failed, or who are not candidates for ASCT or who are not eligible for intensive chemotherapy. Patients who are ineligible for intensive second line chemotherapy must have received at least one prior rituximab-containing combination chemotherapy regimen. The study will assess the safety, efficacy, pharmacokinetics (PK), immunogenicity of the 3 avelumab-based combination regimens tested, and collect patient reported outcome (PRO) data.