Many engineering applications involve the optimization of several contradictory criteria and do not possess an explicit algebraic structure which could be exploited. DMulti-MADS is a multiobjective derivative free optimization algorithm which targets these types of problems. It is based on the Mesh Adaptive Direct Search (MADS) algorithm for single-objective optimization. As a direct search method, its functioning is divided into two parts: a poll and a search. The poll consists in a local exploration around a solution, on which convergence analysis depends. The search is an optional step, more flexible, which practically enhances the performance of the procedure. This talk proposes the integration of quadratic models into DMulti-MADS to improve its performance. New formulations are explored and compared with existing ones. Preliminary numerical results show that these approaches improve the performance of the method, compared to other state-of-the-art algorithms.