If one builds his succah under a tree, it is as though he had built it inside the house.  If a succah [is built] atop another succah the upper one is valid, and the lower one is invalid. R’ Yehudah says: If there can be no tenancy in the upper one, [only] the lower one is valid.

If one spread a sheet over [the s’chach] because of the sun, or beneath it because of the falling leaves, or if one spread it over a four-poster bed, it is invalid. However, one may spread it over a two-poster bed.