In this paper we consider strategies for MIMO interference channels which combine the notions of interference alignment and channel pre-inversion. Users collaborate to form data-sharing groups, enabling them to clear interference within a group, while interference alignment is employed to clear interference between groups. To improve the capacity of our schemes at finite SNR, we propose that the groups of users invert their subchannel using a regularized Tikhonov inverse. We provide a new sleeker derivation of the optimal Tikhonov parameter, and use random matrix theory to provide an explicit formula for the SINR as the size of the system increases, which we believe is a new result. For every possible grouping of K = 4 users each with N = 5 antennas, we completely classify the degrees of freedom available to each user when using such hybrid schemes, and construct explicit interference alignment strategies which maximize the sum DoF. Lastly, we provide simulation results which compute the ergodic capacity of such schemes.