If you already have 3 officers on board, you still can try to recruit a new one. However if you confirm recruitment, he or she doesn't actually join your crew. Your old officers stay with you, and the officer you tried to recruit disappears from the Docks and becomes unavailable. I think the game should ask you to dismiss one of your officers before allowing you to confirm recruitment of a new one.
Ticket #2748 AoP - RFE - Rework Recruiting new officer when already have 3
Just saw that this morning. Got 3 (regular 1st mate, Nathaniel Sveet, and Eric Hawke) and try to recruit Markos Greenmarket, game crashed. The original 3 stayed, no Markos, but yet the Log entry said he joined.
I am going to look for Galda Fenn now that I dump that Eric Hawke..... She joined without issue! Time to look for some Krakens, Ice Demons, etc.