Once all the admission rounds i.e. iterations are completed, it is not possible to switch from one BITS campus to another. A friend of mine got EEE at BITS Hyderabad, and even after a talk with the director he couldn’t manage a switch to BITS Pilani (even though he was ready to take other branches like Chemical Engineering). Once you fill a certain campus as your first preference, there’s no going back.
When iterations are in progress, after the 3rd round, you’ll have to visit the allotted campus to finalize your seat. Upon reaching, you’ll be given a pink form which would ask whether you are willing for a promotion to your preferred campus, in case a promotion is possible. Filling ‘Yes’ is the only way of making a switch possible. I filled in a ‘Yes’ during my time, and consequently, I got switched from E&I at BITS Goa to EEE at BITS Hyderabad.
Thus, according to your situation, you can decide whether a switch is possible for you or not. I have described both the scenarios accordingly.