I was wrong; Jim Keltner did not record w/ Paul.
Matter of fact, there are several musicians who played with three out of four Beatles: drummer Jim (all but Paul), bassist Klaus Voormann (all but Paul), multi-talented Jeff Lynne (all but John), keyboar player Billy Preston (all but Paul).
Worked w/ two ou of four Beatles: drummer Ian Pace (w/ George & Paul), guitarist Hugh McCraken (John & Paul), drummer Andy Newmark (Jon & George), drummer Dave Mattacks (Paul & George)and a bunch of others.
It seems DNITO is right - only the great late Nicky played for all Beatles.[^]