This paper explores the use of combinations of priority rules or greedy heuristics to solve the Quadratic Assignment Problem (QAP). Current solution approaches based on greedy heuristics concentrate on a single selection rule to find a solution for a data set. Many such solution approaches exist. Empirically, it has been observed that no single greedy heuristic is able to provide high quality solutions for diverse data sets, which generates difficulties when selecting a solution method. As an alternative, this paper examines the effects of applying multiple heuristics to a single problem instance. Additionally, this work studies the results of combining multiple greedy heuristics within a meta-heuristic for each problem instance. In this work the results from applying several greedy heuristics to a set of well-know problems are presented and analyzed. Test problem instances were obtained from the QAPLIB. These problems range from 12 to 128 nodes (facilities and locations). The goal of this paper is to study the effects of combining multiple construction heuristics to solve the QAP. The expectation from this study is that the benefits obtained from this approach can be applied to other combinatorial problems.