Multiple AG groups complicated set up question
Nothing additional is required. You would just add server F as another replica for both AG #1 and AG #2 (provided that you do not have collisions in your database names). 

Just remember that they all need to be members of the same WSFC (given the version you are working with).

With 2012 you must have the Windows machines on the same WSFC in order to add them to an AG, as such you will not be able to use the F server for both AGs (you'll have to choose one or the other).