We propose a novel method for user-to-user interference (UUI) mitigation in dynamic time-division duplex multiple-input multiple-output communication systems with multi-antenna users. Specifically, we consider the downlink data transmission in the presence of UUI caused by a user that simultaneously transmits in uplink. Our method introduces an overhead for estimation of the user-to-user channels by transmitting pilots from the uplink user to the downlink users. Each downlink user obtains a channel estimate that is used to design a combining matrix for UUI mitigation. We analytically derive an achievable spectral efficiency for the downlink transmission in the presence of UUI with our mitigation technique. Through numerical simulations, we show that our method can significantly improve the spectral efficiency performance in cases of heavy UUI.