A high percentage of resorts allow this option. However, the "split week" option has definite limitations.
The most significant limitation is that only one of the two stays can be over a weekend. The two stays are generally fixed as Fri-Sun and Mon-Thurs.
You also cannot combine this option with the option to lock off your unit, thus trying to get, for example, four different stays for a single week of ownership.
Further, you can use this option only if there is availability. Obviously, since most people want to reserve for an entire week, Marriott doesn't make much inventory available for this option.
The fee to split your week is $75 (or $29 per night at Custom House, where you can reserve a weekend stay
and individual single weeknights).
For a further discussion of this issue, see
this recent thread.