This disclosure provides systems, methods, and apparatus, including computer programs encoded on computer storage media, for multiple downlink control information (DCI) message handling for multiple control resource set (CORESET) groups. In one aspect, a user equipment (UE) may provide separate or joint feedback for data messages received from different CORESET groups. In some examples, the UE may be configured with code block group (CBG)-based transmissions for a component carrier (CC) or a CORESET group in a CC. If implementing a dynamic codebook, the UE may track separate transport block (TB)-based and CBG-based downlink assignment indexes (DAIs) for each CORESET group or may track joint TB-based and CBG-based DAIs across the set of CORESET groups to handle the CBG configuration. Additionally, or alternatively, if implementing a semi-static codebook, the UE may apply skipping rules across the set of CORESET groups or separately for each CORESET group to reduce signaling overhead.