Classical query optimization compares query plans according to one cost metric and associates each plan with a constant cost value. In this paper, we introduce the multi-objective parametric query optimization (MPQO) problem where query plans are compared according to multiple cost metrics and the cost of a given plan according to a given metric is modeled as a function that depends on multiple parameters. The cost metrics may, for instance, include execution time or monetary fees; a parameter may represent the selectivity of a query predicate that is unspecified at optimization time. MPQO generalizes parametric query optimization (which allows multiple parameters but only one cost metric) and multi-objective query optimization (which allows multiple cost metrics but no parameters). We formally analyze the novel MPQO problem and show why existing algorithms are inapplicable. We present a generic algorithm for MPQO and a specialized version for MPQO with piecewise-linear plan cost functions. We prove that both algorithms find all relevant query plans and experimentally evaluate the performance of our second algorithm in multiple scenarios.