The top-k query is a common means to shortlist a number of options from a set of alternatives, based on the user's preferences. Typically, these preferences are expressed as a vector of query weights, defined over the options' attributes. The query vector implicitly associates each alternative with a numeric score, and thus imposes a ranking among them. The top-k result includes the k options with the highest scores. In this context, we define the maximum rank query (MaxRank). Given a focal option in a set of alternatives, the MaxRank problem is to compute the highest rank this option may achieve under any possible user preference, and furthermore, to report all the regions in the query vector's domain where that rank is achieved. MaxRank finds application in market impact analysis, customer profiling, targeted advertising, etc. We propose a methodology for MaxRank processing and evaluate it with experiments on real and benchmark synthetic datasets.