FWIW, at the UCs, well at least at UC-Berkeley and I’m pretty sure at UCLA (convert 4 semesters to 6 quarters):
transfer students with single majors are allowed four semesters to finish the degree and five semesters for those pursuing more than one majors. Students who do not complete their degree within these semester limits are then subject to the unit ceiling.
This implies that you can take as many units as you want during these 4 semesters / 6 quarters, no limits.