So this is not a question that's particularly easy to answer, partly because of how manning ships worked in this time period and partly because the research we have on it is a bit scanty.

To start with, it's important to define how a man was impressed, and what would happen upon that happening. It was not unknown for complete landlubbers to be impressed, but press gangs usually looked for men in areas where seafarers would be present, and they preferred to press men who had previous experience at sea.

For the most part in this period, captains were responsible for manning their own ships, and though ships newly in commission (more on this later) could rely to some extent on drafts of men from the local port-admiral, many ships also sent out their own press gangs, or relied on the captain's local reputation to bring in volunteers. There were sections of the seafaring population that were immune to pressing (whalers, for example) and men who agreed to give up a quota of seamen per year in return for protection against being impressed en masse (bargemen on the Tyne and Wear).

Underlying all of this is the fact that impressment was not necessarily as coercive as we tend to perceive it, and that it was almost always a negotiation between the men being pressed and the men doing the pressing. It was a bit of a universal truth in the Navy that long-standing seamen (warrant and petty officers) had usually been impressed themselves, and that promises of promotion were used as inducements for impressment, or as conditions -- "join voluntarily and we can rate you able, but if we impress you you'll be rated a landsman" -- that sort of thing. Impressment took different forms over time, and the term started with an "imprest" or "prest" that was given to men to secure their employment, in the period of the Dutch wars.

Anyhow, once a man were to be impressed or to join up, he was sent to a ship's company. The pre-modern Royal Navy differs from modern navies in an important regard, which is that there was no such thing as a fixed period of service in the Navy. Men would be assigned to a ship for the duration of a cruise or a voyage, rather than for a term of service that they could be reassigned during (that didn't start until the 1870s or so). That also means that men existed on a ship's books, not in any sort of central naval registry or list of seamen. (Officers -- commissioned and warrant -- had this sort of thing due to seniority, but that's a different story.) At the end of a commission -- which could last for a season or a few years -- ships would be paid off, and men could choose to re-enlist, enlist on a different ship, seek merchant employment, or leave the Navy (note that this would not remove them from the pool of manpower the Navy recruited/impressed against.)

Men would fairly regularly switch from ship to ship, either by deserting one ship for another with a more congenial quarterdeck, or to be with friends, or in occasional transfers, sometimes with the consent of the officers, and sometimes without it -- in which case they would be marked as deserters on a ship's books, though there was often not an incentive to pursue deserters in the same way that the RN pursued mutineers or the like. There was also an issue where men inadvertently left behind when ships sailed would be counted as deserters and punished -- there were calls to reform this practice throughout the period. But we unfortunately don't have statistics for how many ships a man might serve on.