Plectic Stark–Heegner points were recently introduced to explore the arithmetic of higher rank elliptic curves: the concept was inspired by Nekovář and Scholl’s plectic philosophy, while the construction is based on Bertolini and Darmon’s groundbreaking use of the p-adic uniformization of Shimura curves to study the Birch–Swinnerton-Dyer conjecture. In this note we present a framework based on the non-Archimedean uniformization of higher-dimensional quaternionic Shimura varieties which can be used to describe plectic Heegner points geometrically. To this end, we define the category of Mumford varieties, that is, varieties that can be uniformized by products of certain analytic subsets of \(\mathbb {P}^1\) , and construct the plectic Jacobian functor from the category of Mumford varieties to the category of topological groups extending the classical Jacobian functor on Mumford curves.