Yes there is a history of pilots swapping seats - it is actually very common and I have done so myself. I was previously a turboprop training captain and am now a jet First Officer which is a very common thing. As you will be aware, most airlines promote people on seniority which means that those who have been there the longest get first crack at the good deals! Whatever your previous history when you join a new company is by and large unimportant - you just join the bottom of a long seniority list and hope for expansion of the company or that a lot of people above you leave or retire! People like me just have to wait for a slot to come up and apply for it. Assuming you are basically suitable (passed all you route check flights and simulator checks to a sufficient standard) then you get put on another command course.
In somewhere like BA, it is common for someone to be a captain with his previous company on a 737, and then to give it all up to be an FO for several years on joining BA. Eventually, he may then elect to be a 737 captain again or to be an FO on 747s for years. He may even elect after some time to be an Airbus captain before going back to being a 747-400 FO and so it goes on. Seniority is King, and the higher up the list you are the greater your choices - particularly in the big airlines like BA, Lufthansa, Air France, United Airlines, American Airlines and so on.
As I have said previously, however, the name of the game is to get into the left hand seat. For some reason (human nature I guess!), there is a widespread perception that the bigger the jet the better the deal! For example flying 747s is widely considered more prestigous than flying 737s. Such is life!