  We prove a deformation theorem for prismatic higher $(G,\mu)$-displays over
quasi-syntomic rings. As an application, we extend the classification of
$p$-divisible groups via prismatic Dieudonn\'e modules to a class of rings
properly containing quasi-syntonic rings. Finally, we related the stack of
prismatic higher $(G,\mu)$-displays to integral local Shimura varieties.
