If you want to apply different texture to some elements, simply apply a different material to those objects. Theres no need to create a new uv set, you can continue working on the existing uv set, in fact creating a new uv set will likely complicate things.
If you want to isolate certain objects, create a new mesh object and cut and paste those elements into it.
If you need more than 1 uv set for a single object, for instance if you have a standard uv set and you need a lightmap uv set, go to lists -> uv maps -> new map.
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If you want to apply different texture to some elements, simply apply a different material to those objects. Theres no need to create a new uv set, you can continue working on the existing uv set, in fact creating a new uv set will likely complicate things.
If you want to isolate certain objects, create a new mesh object and cut and paste those elements into it.
If you need more than 1 uv set for a single object, for instance if you have a standard uv set and you need a lightmap uv set, go to lists -> uv maps -> new map.
Body in one UV map
Arms in another
And background elements in the third map
It sounds like you simply need to separate each group into a different mesh object.