This work presents a distributed model predictive control strategy for generating collision-free point-to-point motions for a formation of multiple vehicles. It extends a synchronous distributed model predictive control (DMPC) scheme presented in earlier work that allows violations of the formation requirement when necessary, for example to avoid suddenly appearing obstacles or to move through narrow passages. In order to obtain safe motion trajectories during these violations, the current paper presents an approach for including inter-vehicle collision avoidance constraints in the DMPC scheme. The collision avoidance is achieved by separating each pair of vehicles by a shared hyperplane and two methods are proposed for updating the separating hyperplane over the DMPC cycles. Simulations with formations of holonomic vehicles demonstrate the capability of the presented strategy.