  Using a mixed-characteristic incarnation of fusion, we prove an analog of
Nekov\'a\v{r}-Scholl's plectic conjecture for local Shimura varieties. We apply
this to obtain results on the plectic conjecture for (global) Shimura varieties
after restricting to a decomposition group. Along the way, we prove a $p$-adic
uniformization theorem for the basic locus of abelian type Shimura varieties at
hyperspecial level, which is of independent interest.
