Marriott T&C:

2.1.b. Qualifying Charges. “Qualifying Charges” are:

i. Charges incurred during a stay in a guest room at a Participating Property by a Member on their folio and up to two (2) additional guest rooms with same check-in and check-out dates, including, without limitation, charges for:


So you definitely get the points for up to 3 rooms at a time.

However, 2.1.d(ii) states:

ii. A “Qualifying Stay” is a credit pursuant to these Program Rules that counts toward earning Elite Night Credit. Except as otherwise noted in Section 4.2, Members will only earn credit for each Qualifying Night (i) which is part of a Stay at a Qualifying Rate (as described in 2.1.e.), for the guest room the Member personally pays for and stays in, and not for any additional guest rooms


So no, you should not count on getting the nights for extra rooms.