First-in-human Dose Escalation and Expansion Study With the SIRPα-directed Monoclonal Antibody BYON4228

Inclusion Criteria: * Part 1 (dose escalation): B-cell NHL expressing CD20 by immunohistochemistry (IHC) or flow cytometry, relapsed/refractory (R/R) to at least 2 prior lines of therapy. * Part 2 (dose expansion): A. Histologically confirmed diffuse large B-cell lymphoma (DLBCL) or Mantle Cell Lymphoma (MCL) expressing CD20 by IHC or flow cytometry, R/R to frontline therapy. B. Histologically confirmed marginal zone or follicular lymphoma (Grade 1-3a) expressing CD20 by IHC or flow cytometry, R/R to at least 2 prior lines of therapy. * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 1; * Adequate organ function; * Laboratory measurements, blood counts (Growth Factor (GF) support and blood transfusions are not allowed within 2 weeks prior to this assessment): * Hemoglobin ≥ 8.5 g/dL (\> 5.28 mmol/L); * Absolute neutrophil count (ANC) ≥ 1.0 × 10\^9/mL; * Platelet counts ≥ 50 × 10\^9/mL; Exclusion Criteria: * Having been treated with CD47 or SIRPα targeting agents at any time or other anticancer therapy within 4 weeks or as defined in the protocol; * History of hypersensitivity or allergic reaction to any of the excipients of BYON4228 or rituximab which led to permanent discontinuation of the treatment; * Burkitt's lymphoma; * Red blood cell (RBC) transfusion dependence; * Patients with active graft versus host disease (GVHD) or ongoing immunosuppression for GVHD; * History of autoimmune hemolytic anemia or autoimmune thrombocytopenia; * History of active autoimmune disorders (including but not limited to: Crohn's disease, rheumatoid arthritis, scleroderma, systemic lupus erythematosus, Grave's disease) or other conditions that compromise or impair the immune system (except for hypogammaglobulinemia); * History (within 6 months prior to start IMP) or presence of clinically significant cardiovascular disease such as unstable angina, congestive heart failure, myocardial infarction, uncontrolled hypertension, or cardiac arrhythmia requiring medication; * Currently diagnosed or suspected CNS involvement; * Severe active infection or other severe uncontrolled systemic disease (e.g. advanced renal disease, pulmonary, uncontrolled diabetes mellitus, severely immunocompromised state, or metabolic disease)