But note that engineering majors require getting started in the prerequisite courses early to avoid closing off the possibility of doing them, even at schools which do not have capacity limitations on those majors.
Capacity limitations on engineering majors are most likely to be found at larger schools of relatively high admission selectivity that enroll their engineering majors to capacity. This tends to describe popular state flagships the most. Very wealthy (typically among the most selective) private schools can afford to maintain unused reserve capacity to allow changing majors without difficulty, while less selective schools usually do not have so many students able and willing to handle the rigor of engineering majors that they hit capacity.