To support alternative positioning, navigation and timing (A-PNT), multi-DME with better geometry than distance measuring equipment (DME)/DME can be used to improve the performance. Different from the existing station selection methods that have been proposed for DME/DME, a station selection method for multi-DME should be considered in order to prevent unnecessary emission of navigation signals because DME receivers have limited number of channels and constrained real-time processing power, and also to limit DME to GNSS L5/E5a interference. A heuristic algorithm is constructed to determine the quasi-optimal selection of DME stations based on geometrical and computational cost restrictions, which is different from a brute-force method checking all possible subsets and selecting the best one. A station selection method for multi-DME is proposed based on the heuristic search. Meanwhile, the degradation of GNSS L5/E5a signal processing that is caused by DME signals is discussed. An advanced station selection method where the DME to GNSS signal interference is taken into account is also proposed. The experimental results show that the methods based on heuristic search can effectively select the quasi-optimal subset of DME stations with less computational expense.