We say that two posets are "doppelgängers" if they happen to have the same number of plane partitions of height k, for any k. We synthesize M. Haiman's rectification, H. Thomas and A. Yong's minuscule K-theoretic Schubert calculus techniques, and a remark made by R. Proctor to give a framework for combinatorial proofs of such poset coincidences. This is joint work with Zachary Hamaker, Rebecca Patrias, and Oliver Pechenik.