Furthermore during the period where the houses of Luxembourg and Habsburg were rivals for the position of dominant house in the empire, some of the Luxembourg rulers gave several Swiss territories in the traditional sphere of influence of the Habsburgs privileges.
Alternatively I wonder, what would have happened if duke Rudolf II of Habsburg (son of Roman-German king Rudolf I of Habsburg and father of John Parricida) hadn't died at the age of 19. Which would have made the implementation of the treaty of Rheinfelden more likely. In which Rudolf II had to waive his rights on Austria & Styria to his older brother Albert I of Habsburg in exchange for (parts of) the Habsburg ancestral lands. Later Rudolf II was appointed duke of Swabia (which had become mostly honorific; in theory it gave ducal authority in Swabia, in practice he would have start to expand his authority from the territories ruled by him, which were supposed to be the Habsburg ancestral lands in Aargau, Sundgau, Breisgau etc.) by his father king Rudolf I.
So a split between a senior Austrian Habsburg (Albertine) branch and a junior Swabian Habsburg(Rudolphine) branch might be interesting.
This Swabian branch stay much more focussed on this region.
The division will look like this:
(Austrian branch: dark purple; Swabian branch: light purple)
(Although I did already suggest this in previous no Switzerland thread)