From what I’ve read, I think they were actually working together on plenty of songs up until the end of 1964 or so.
My understanding is that even up to that point, Paul or John, would bring in a nearly completed song idea for the band to complete, and after that it became a PURELY separate endeavor.
However, none of this is to minimize the various small, but essential tweaks contributed by the band itself during the recording sessions, including Fifth Beatle, producer George Martin.