We propose an elitist Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristic algorithm, called mGRASP/MH, for approximating the Pareto-optimal front in the multi-objective quadratic assignment problem (mQAP). The proposed algorithm is characterized by three features: elite greedy randomized construction, adaptation of search directions and cooperation between solutions. The approach builds starting solutions in a greedy fashion by using problem-specific information and elite solutions found previously. Also, mGRASP/MH maintains a population of solutions, each associated with a search direction (i.e. weight vector). These search directions are adaptively changed during the search. Moreover, a cooperation mechanism is also implemented between the solutions found by different local search procedures in mGRASP/MH. Our experiments show that mGRASP/MH performs better or similarly to several other state-of-the-art multi-objective metaheuristic algorithms when solving benchmark mQAP instances.