Is it possible to animate a single mesh as if it were multiple objects? I am attempting to animate a single mesh which appears as a group of separate objects.
I want to animate three separate boxes which are joined together as a single mesh for ease of use in the dope sheet/action editor. This makes exporting the actions into GLTF easier for action manipulation/programming in three.js.

When I join armature bones to the single box object, I am able to manipulate/pose each object independently. However, when I join the objects together into one mesh, I lose the ability to independently manipulate them, and the bone pose influences all other objects.

Is it possible to join the three boxes together as a single mesh, and independently pose each box within the mesh as if it were its own object? This would make things much easier for exporting to three.js.
I don't think it's possible to add more than one armature to a single object (haven't tested it, though).
What you can do is create all three bones inside a single armature and then parent the mesh to the armature with automatic weights. I think it'll weight properly, but if it doesn't just manually edit the weights so all the vertices in each box are only affected by its respective bone.
I don't know if that helps for your specific needs.