You can run two sets of speakers in series off of a single set of outputs and it will drop the resistance (two 8 ohm speakers in series is a 16 ohm load). So it would work fine from an amplifier compatibility stand point. The possible problem with this would be that both rooms would be on at the same time and would be linked to the same volume control. This would apply to any integrated with only one set of speaker outputs.
Moving to an integrated with an A/B speaker selection switch would allow you to run one set at a time or both sets together, but again it would all be controlled by the same master volume. The Yamaha AS-301 is a nice affordable integrated with A/B speaker outputs.
The other option would be to add a cheap zone control switch that gives you volume control to each zone/room.https://www.monoprice.com/product?p_id=38165&gclid=Cj0KCQjwwLKFBhDPARIsAPzPi-IJ_5JCuFi6K41l9X64C...
I have never personally used a switch like this $29 monoprice one so someone else can chime in if I am overlooking anything but with one of these inline, it wouldn’t matter if the integrated you get has multiple speaker outs. You would have independent volume control over each room.