I kept giving the fertile potion, and then the very fertile one (nature faction), hoping for triplets. I bred a father of twins with a mother of different twins. Still no luck.
Then a mama put her baby down and ran for a guy before I could stop her. I ripped them apart, too late, and there she stood with a triple bundle! No potion or putting the dad on parenting first.
Dad was a twin himself, but it probably had nothing whatsoever to do with it. I think I just got lucky.