The world is rarely static -- many problems need not only be solved once but repeatedly, under changing conditions. This setting is addressed by the "multistage" view on computational problems. We study the "diverse multistage" variant, where consecutive solutions of large variety are preferable to similar ones, e.g. for reasons of fairness or wear minimization. While some aspects of this model have been tackled before, we introduce a framework allowing us to prove that a number of diverse multistage problems are fixed-parameter tractable by diversity, namely Perfect Matching, s-t Path, Matroid Independent Set, and Plurality Voting. This is achieved by first solving special, colored variants of these problems, which might also be of independent interest.