Formally though, it is one bite of the cherry only: once you have accepted a rerouting you can't then change it, and that is in the customer guidelines too. So if an agent said "no more changes possible" then that is the correct position. Hence the advice up in this thread and in the Irrops signposts thread to not rebook things immediately but to wait and see what happens. I know some travellers don't like the uncertainty of that, but with a large company like BA it can take a while for options to become apparent.