  We develop tools to study spaces of $p$-divisible groups and Abelian
varieties with additional structure. More precisely, we extend the definition
of parahoric (Dieudonn\'e) $(\mathcal{G}, \mu)$-displays given by Pappas to not
necessarily $p$-torsionfree base rings and also introduce the notion of an $(m,
n)$-truncated $(\mathcal{G}, \mu)$-display. Then we study the deformation
theory of Dieudonn\'e $(\mathcal{G}, \mu)$-displays.
  As an application we realize the EKOR stratification of the special fiber of
a Kisin-Pappas integral Shimura variety of Hodge type as the fibers of a smooth
morphism into the algebraic stack of $(2, 1\text{-}\mathrm{rdt})$-truncated
$(\mathcal{G}, \mu)$-displays.
