What is wrong with CPP?
You can get an idea of how competitive admission to the various majors at the various UCs is for junior transfer admission at https://www.universityofcalifornia.edu/infocenter/transfers-major .
Private schools vary in transfer admission selectivity. USC takes lots of transfers, but mostly from community colleges (like UCs and CSUs), according to http://admission.usc.edu/transfer/prospective/transferprofile.html . Stanford takes very few transfers, apparently heavily from non-traditional backgrounds.