I do not think it is possible if not using tricks that however complicate the management of solid (e.g., giving the surface a thickness of 0.001 allows to obtain the same solid divided into two)
I don't know what you have to do, but you could do that:
create the complete solid
cover it and paste it with connection (renamed in solid upper part) and cut it with the surface
cover and paste another with connection (renamed in solid lower part) and cut with the same surface
if you have to make a change that affects both the top and bottom run it on the full solid, all other variations do it or on the top or bottom solid.