A two story Sukkah:
If one built a Sukkah on top of another Sukkah then if the floor of the top Sukkah, which serves also as the Sechach for the top Sukkah, is able to support pillows and blankets [and a person eating and sleeping], then although the top Sukkah is valid, the bottom Sukkah is invalid.
The reason for this is because: The Torah states “In Sukkos you shall dwell” in singular form, omitting the letter “Vav”, thus teaching that one may only fulfill the Mitzvah within a single Sukkah and not within a double Sukkah.
If the top Sukkah is itself invalid: If the top Sukkah was invalid such as its Sechach did not give off majority shade, or it was not ten Tefach [80cm.] from its floor [which serves as the Sechach of the bottom Sukkah], then the bottom Sukkah is valid even if it only has majority shade with the joint shade of the Sechach of the top Sukkah. If however the top Sukkah reaches twenty Amos high then although it itself does not invalidate any of the Sechach directly under it, nevertheless it itself cannot be used to join the majority of shade that is required.
May one have a Sukkah made with two layers of Sechach one over the other?
If the two layers of Sechach are ten or more Tefach [80cm.] apart, and the lower Sechach is sturdy enough to support pillows and blankets, then it is viewed as a two story Sukkah and the Sukkah is thus invalid.
May one eat in a Sukkah which has the Sechach of an upper Sukkah protruding over it?
If the bottom Sechach is firm enough to hold a person lying on pillows and blankets: This matter is disputed by Poskim. Some Poskim hold that it does not invalidate the Sechach directly under it being that this protruding Sechach has no walls. Others however rule that despite the above it does invalidate the Sechach under it. Practically one is to be stringent and avoid this situation.
If the bottom Sechach cannot hold a person lying on a pillow: The lower Sukkah is completely valid.