I summon 4 NoAI foxes in Sitting, Sleeping, Crouching, and normal state.

When the fox with Crouching:1b NBT tag is in the scene or rendered, it will affect all the other foxes animation.

Although those foxes' NBT tags are Crouching:0b, they all sway their bodies, just like the one with Crouching:1b NBT tag. 

In the background, there're 4 NoAI foxes, and those 3 in foreground are alive. All of them will shake their body.