Rate-Splitting (RS) has been proposed recently to enhance the performance of multi-user multiple-input multiple-output (MU-MIMO) systems. In RS, a user message is split into a common and a private part, where the common part is decoded by all users, while the private part is decoded only by the intended user. In this paper, we study RS under a phase-shift keying (PSK) input alphabet for multi-user multi-antenna system and propose a constructive interference (CI) exploitation approach to further enhance the sum-rate achieved by RS under PSK signaling. To that end, new analytical expressions for the ergodic sum-rate are derived for two precoding techniques of the private messages, namely, 1) a traditional interference suppression zero-forcing (ZF) precoding approach, 2) a closed-form CI precoding approach. Our analysis is presented for perfect channel state information at the transmitter (CSIT), and is extended to imperfect CSIT knowledge. A novel power allocation strategy, specifically suited for the finite alphabet setup, is derived and shown to lead to superior performance for RS over conventional linear precoding not relying on RS (NoRS). The results in this work validate the significant sum-rate gain of RS with CI over the conventional RS with ZF and NoRS.