Is it legal to use the Family Growth action to extend your family by 2 or even 3 if you have enough rooms? The rules do not forbid it, but they only talk in singular about the new family member.
You can add at most one newborn regardless of the number of empty rooms you might have.
The rules are clear on this:
After Family Growth, also 1 Minor Improvement (Stage 2): A player may only use this Family growth space if he has more empty rooms than Family members.
A player who chooses a Family growth action adds their newborn offspring to the Action space In the Return home phase, the new Family member is taken home ... A Player who takes the Family growth action will therefore have one additional (adult) Family member to use from the following round onwards.
Each 'Family Growth' action gets you one additional person. You can do more than one 'Family Growth' action in a turn (getting multiple people) if the spaces are available.