Hi ,
Yes you can do this. This is referred to as a Multi-Sub-Object.
It’s not using multiple UVs though. It’s still using a single UV for the texture but you can layout your UVs to overlap but they’ll use a different texture and not be affected by the other UVs with different textures.
https://www.youtube.com/watch?v=ZiGmbH8nl_A
This video is a good start for Mult-Sub-Object.
While this doesn’t show how to handle the UVs overlapping I can explain it a little better with an example I did from my schools final project a while back.
In this I had the texture laid out with everything but the screen using the entire texture space (512x512). The screen was using the same texture space (essentially overlapping in the UV 1 slot), but I made it take up the entirety of the UV window to hold the entirety of the 512x512 texture space. With it being set in Max as Material ID 2 I could have it use the same texture space without needing a new UV. This is all because of how the material IDs are set up.
If you need a clearer example let me know and I’ll throw something together to explain it better. 
Tim