I haven't seen this proposed yet.
A system, similar to our current system of a President & Vice President, and Senate (at least partially elected by the regions), but everyone else would then be part of the lower house. Governors would be members of the lower house but ineligible for the upper house. Cabinet members would come from the lower house. An election for Speaker of the House would be held at the same time as the other federal elections. I would also consider having regional Senator elections administered by the regions.
Might be a little too American based for some of you though.