Originally Posted by
LondonAussie
As for changing your FF program between flights, this should be possible by loading your booking into the Finnair or RJ sites and first removing your BA EC number and then adding your other program number. I would also make sure to keep a copy of your boarding pass in case you need to manually claim.
Alternatively, CX allows you to do that on their website (and app, even) as to who to credit for each specific flight in the same booking.