We establish new capacity bounds for the multi-sender unicast index-coding problem. We first revisit existing bounds proposed by Sadeghi et al. and identify the suboptimality of their inner bounds in general. We then present a simplified version of the existing multi-sender maximal-acyclic-induced-subgraph outer bound. For the inner bound, we propose joint link-and-sender partitioning to replace sender partitioning in partitioned Distributed Composite Coding (DCC). This leads to a modified DCC (mDCC) that outperforms partitioned DCC and suffices to achieve optimality for some index-coding instances. We also propose cooperative compression of composite messages in composite coding to exploit messages common to different senders to support larger composite rates than those by point-to-point compression in the existing schemes. We then develop a new multi-sender Cooperative Composite Coding (CCC) scheme. CCC further improves upon mDCC in general, and is instrumental to achieve optimality for a number of index-coding instances.