I'm not referring to the number of officers assigned to a ship based on the number and type of available consoles. Just in the general pool of available officers.
I had an officer candidate offered to me after skilling up and I accepted his commission but he disappeared. I was wondering if that was because I had too many officers already (4 at Lt. Grade 9).
Yes, there's a limit. At Lieutenant, it's 4 officers. At Lieutenant Commander, it's 6. I'm not sure if it continues scaling up with 2 new officers every rank, or not, but that seems likely at this point. From what I gather, you have enough officers to be able to fit out two different ship classes by the time you hit Admiral, or have a full Ship compliment and an Away Team setup at the least.
The officer in question MIGHT still be in your Requisitions tab, though, under Assignments. And as far as I know there's no limit to how many officers you can have in the Requisition tab (to use as training up or trading as you prefer).
...More advanced information is appreciated, of course.