  We propose a conjectural construction of global points on modular elliptic
curves over arbitrary number fields, generalizing both the p-adic construction
of Heegner points via Cerednik-Drinfeld uniformization and the definition of
classical Stark-Heegner points. In alignment with Nekovar and Scholl's plectic
conjectures, we expect the non-triviality of these plectic Stark-Heegner points
to control the Mordell-Weil group of higher rank elliptic curves. We provide
some indirect evidence for our conjectures by showing that higher order
derivatives of anticyclotomic p-adic L-functions compute plectic invariants.
