How can I have multiple separate texture maps for separate objects? Is it possible? I'm new to blender and trying to model a character, but I still don't have a full understanding of UV maps and texturing yet. He's got quite a few parts, so I was doing my best to fit everything onto the one UV map, but I decided to separate a couple of parts of him - namely his ears and wings - so that I could texture those separately, without having to fit them onto the main UV map. Here's my workspace.

I've done extensive googling but still can't figure out the answer to my question - Can I actually have separate textures/UV maps for separate objects? To be clear as possible, I have most of his mesh in an object called HeadBody. I put his ears and wings into another object called EarsWings. I want to texture each separately, but every way that I try to, even when adding a new UV map, it just ends up on the same crowded UV map again when I go into Texture Paint mode. I read a few things about assigning different Materials, but I couldn't figure out how to assign a texture to those Materials.
Any enlightenment is super appreciated. Thank you!
Yes, it's possible. If you have the wings and ears in a separate object, just create a new material, and select there the image texture you want.
The relationship is the following: Object → Mesh → Material → UVMap → Image Texture.

A mesh can have more than 1 material. In the Edit mode you can select faces and assign them to a material in the material tab.

In the Image Editor you can select the texture images to inspect them or paint on them.

In the Texture Editor, the UV map and the texture are specified in the Texture Slot settings. Blender can read this pair from the material or you can specify the there. This defines on which image and where the pixels go when you paint on the 3D model, and vice versa.

In the Shader Editor you can define with nodes the UV Map and the Image Texture that a material uses.

And in the Object Data Properties &gt; UV maps you can select the active (default) UV map for the viewport and for the render.