I would like to model a protein with multiple chains (A,B,C,D) as an
entire rigid body.
Unfortunately I cannot find a way to do this, it seems like that a rigid
body can only contain one protein chain.
Sure, that's straightforward. A rigid body is simply represented
internally as a set of particles - it doesn't care whether those
particles are in the same chain or different chains. You don't say how
you're doing the modeling, but if you're using a PMI topology file, just
use the same rigid body number for all of the domains.