Approximately 81 patients with relapsed or refractory CD32b positive B-cell lymphoma or leukaemia will be entered into this study. This will include approximately 19 recruited for the BI-1206 dose escalation phase (Part A), up to 12 (likely 6) for a combination dose escalation and up to a further 50 patients recruited to two dose expansion cohorts; one of BI-1206 alone and one of BI-1206 plus rituximab (Part B). The final number will depend on the number of dose escalations required to reach the MTD.