A Phase 1 Study of SynKIR-310, Autologous T Cells Transduced With CD19 KIR-CAR, in Participants With Relapsed or Refractory B-Cell Non-Hodgkin Lymphoma.

Inclusion Criteria: - Adult 18 years of age and older. - Histologically confirmed diagnosis of B-NHL before enrollment. - Must have received prior CAR T or were unwilling/unable to receive prior CAR T. - Must have refractory or relapsed disease after receiving 2 prior lines of therapies. - If relapsed/refractory post-auto-SCT, then must have undergone auto-SCT at least 6 months prior to enrollment. - If relapsed/refractory disease after allogeneic stem cell transplant (allo SCT) then must have undergone allo-SCT at least 6 months prior to enrollment and without evidence of graft versus host disease. - Measurable disease at time of enrollment: At least one measurable lesion per Lugano Response Criteria (Cheson et al., 2014). - Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1 Exclusion Criteria: - Previously treated with any investigational agent within 30 days prior to screening. - Adequately treated non-melanoma skin cancer such as basal cell or squamous cell carcinoma - Carcinoma-in-situ (e.g., cervix, bladder, breast) treated curatively and without evidence of recurrence for at least 3 years prior to enrollment. - Any other malignancy which has been completely treated and remains in complete remission for ≥ 5 years prior to enrollment. Completely treated prostate cancer with prostate-specific antigen (PSA) level < 1.0 may also be permitted. - Known immunodeficiency disease. - History or presence of active or clinically relevant primary central nervous system (CNS) disorder, such as seizure, encephalopathy, cerebrovascular ischemia/hemorrhage, cerebellar disease, or any autoimmune disease with CNS involvement. For primary CNS disorders that have recovered or are in remission, participants without recurrence within 2 years of planned study enrollment may be included. - Uncontrolled hypertension, history of myocarditis or congestive heart failure, unstable angina, serious uncontrolled cardiac arrhythmia, or myocardial infarction within 6 months prior to study entry. - Any active uncontrolled systemic fungal, bacterial or viral infection. Note: Other protocol defined Inclusion/Exclusion criteria may apply.