I’ve heard for huge VFX productions (Lord of the Rings, Transformers, etc) it’s common for models to feature many hi-res textures per model. But I’ve never done that personally. For one texture space per character, I’ll typically go as high as 4K texture resolution (4096 x 4096 pixels). I think 8K (8192 x 8192 pixels) is possible and workable with Blender…though never tried it I don’t think.
Often my character models are broken into multiple objects (body, clothing, sword, shoes, etc) and it’s not uncommon to do individual textures for each object, which is kinda like multiple textures per character.
I was told that the rule for texture resolution is to double the resolution of the final output of the project. For example, if I’m making a short film at 1920 x 1080 (1080p), my models’ texture resolutions should be 4K (double the highest dimension in output format).
My brother works for Hi-Rez Game Studio (Smite, Paladins) and they use normal maps with hand-painted textures.