MIT accepts very few transfer students. Transferri
ng to MIT is exceptionally unlikely.
MIT is also one of the most academically challenging universities in the world. If you are currently doing well at Caltech, and want a major that Caltech does not offer, then you might both have a very good reason to transfer to MIT and be academically ready to take on the challenge. Otherwise, arriving as a junior at MIT might be a significant shock from an academic point of view. This might be a big part of why MIT accepts so few transfer students.