You cannot start your CPT in your new major until you complete at least a semester. If you are going into higher degree in a same major, of course you can. It all depends on professor, if he/she allows you to go in CPT or not. Since your professor has to mention that the CPT is required in order to complete your degree, your nature of work at your CPT must be directly related to your major. Your professor and your Int'l student advisors are the ones who approve/reject your CPT, so its better to talk to them and convince them the need for CPT.