For planning, you need numbers.
Plot, development plan, house, capacity, account.
And you need expertise.
Most likely, you don’t need to separate triplets in the first few years. However, I only know it from some twins: they must not be separated and have a strong bond.
In this respect, I would say you have a 5-year buffer. Maybe you can use this time to see whether the triplets need each other or not.
If ultimately four children’s rooms are needed, one possibility would be to reduce the size of the two existing children’s rooms and create an access between them to a third gable, where a new room would then be created. Below that, a bay window would be created in the dining area. Of course, the third gable can be made larger or wider so that an L-shaped house is created.
I would clad the annex or extension in white wood.
Otherwise, I also see the possibility of using the office downstairs as a laundry room/dressing room/storage, from where you can go into an annex where the parents' wing would be.
I don’t see an overbuild of the garage because of the clearance spaces.