In this paper we address the problem of post-processing position constrained plans, output by many of the recent efficient metric temporal planners, to improve their execution flexibility. Specifically, given a position constrained plan, we consider the problem of generating a partially ordered (aka "order constrained") plan that uses the same actions. Although variations of this "partialization" problem have been addressed in classical planning, the metric and temporal considerations bring in significant complications. We develop a general CSP encoding for partializing position-constrained temporal plans, that can be optimized under an objective function dealing with a variety of temporal flexibility criteria, such as makespan. We then propose several approaches (e.g. coupled CSP, MILP) of solving this encoding. We also present a greedy value ordering strategy that is designed to efficiently generate solutions with good makespan values for these encodings. We demonstrate the effectiveness of our greedy partialization approach in the context of a recent metric temporal planner that produces p.c. plans. We also compare the effects of greedy and optimal partialization using MILP encodings on the set of metric temporal problems used at the Third International Planning Competition.