If I have a character and a basic rig for the body, sound I have a facial rig that’s separate or part of the same armature? How would I go about this? 
I think it’s best to keep the facial bones with your main rig. While you can have multiple rigs parented or connected in some way, I often find that makes things more complicated.
So make your facial bones a part of the same rig as the body, and put them in their own bone group and layer. You can then pick a color theme for your bone group to more easily see them. And when you put them in a layer, you can turn there visibility on and off. Just like an object layer. This is for me, a cleaner way to work with things.
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Part of the same armature is, in general, better. It’s easier for the animator to use and is simpler. But sometimes, generally for ease of mix/match or other editing concerns, you’ll want to use separate armatures.
If you want to do separate armatures, you can do that, but there are things to be careful of.
The best way to do it is to create an artificial, non-deforming, binary (1.0 or 0.0) vertex group and assign all verts that are part of your “face” to it. Then, figure out all bones from your body armature that are used to deform any of the margins of this area-- hopefully, that’s only your head bone, but it could easily include your neck bone-- and duplicate them to your face armature, with copy world-space transforms from your body armature. Finally, you have two armature modifiers, order doesn’t matter, modulated by your binary vertex group or the inversion of it.
Multimod is bad because 1) it leads to volume loss at soft transitions 2) it’s totally unnecessary unless you have soft transitions and 3) for whatever reason it requires backwards vertex groups for the modifier.
Don’t just parent your face armature to your body’s head bone; bone transforms are measured in local space, not world space. Face armature should be parented to body armature, with its root bones copying transforms from body-armature counterparts instead.
The model I’ve been describing has the face armature acting as a child of the body armature, but you can reverse that if you want.
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Don’t make your life harder. There is no reason to separate face rig from body rig. Just use bone layers to easily hide\show needed parts.
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Thank you all for your advice! I apologize for the late reply. It seems that having one rig was the best option.