I'm not exactly sure what you mean by overlap the UVs, but I did paint well past the edges of the mapped UV's. The problem isn't that the painted area of the texture file ends short of the mapped area, it's with that black mask Maya automatically puts over the area around the UVs when the material file is attached to a mapped object.
The only place you see it is in the UV Texture Editor (and occasionaly on the model-like in this instance)