Well, modern sonars can track a wide array of targets thanks to numeric technologies. I'll guess most modern subs sonars can track an infinite number of targets, but as far designation goes, I don't see a system going over 99. Think of it, tracking more than 10 contact at a time is already a hell of a job for the sonar operator, not speaking of the TMA specialist.
Some european TCS I know of can keep dozens of live TMA solution, about the same amount in "hidden" state (the operator can't see them, but can call them back for future reference) as well as recalling a previously deleted track to start over (assume you've lost contact for some hours, you delete it to gain some space, but you take it back, so call back the previous bearing to start a new solution)
As for FCS, generally you have one Firing solution per tube, add some "standby" if you need to keep track of a solution for a secondary target, and you're about it.
Hope it satisfies your curiosity.
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