Almost every player with a substantial career in major league baseball plays for more than one major league team over his career. The only Mets to accumulate at least 500 plate appearances over his career as a Met, and then going on to retire without also at some point playing for another major leage team, have been Ed Kranepool, Ron Hodges, Bruce Boisclair, Rod Kanehl and the Twins' current manager, Ron Gardenhire. The only pitchers to pitch at least 162 innings for the Mets and retire having played only for the Mets are Bob Apodaca, Jeff Innis, Eric Hillman and Rick Baldwin.
Far more frequent are the players who play for mutiple teams over a career. For example, 120 Mets also played, at some point in their careers, for the Dodgers. That's the highest number of players the Mets have shared in common with any single franchise. The top 5 franchises, in terms of the number of players who played for the franchise and also the Mets at some point, are:
Dodgers, 120 players
Cardinals 114 players
Cubs 106 players
Padres and Yankees: 101 players
The franchise with the fewest players who also played for the Mets at some point in their careers is the Diamondbacks, with only 25 players who were future or past Mets. of course, that's not quite a fair comparison because the D-backs have only been around for 10 seasons, compared to the 46 seasons teams the Mets and Dodgers (and other teams dating back to 1962 and before) have had in common. In fact Arizona is quite close to the Dodgers if you look at average players in common with the Mets on a per common season basis. With 120 players, over the 46 years the Mets franchise has been playing, who have also played for the Dodgers, that averages out to 2.6 players per season of the two teams' common existence. With 25 common players over ten years, the Mets and D-Backs have averaged 2.5 common players per season. Using this method, the Rockies, with 54 players who have also been Mets, over just 15 years of the Colorado franchise's existence, have the highest per season average of any franchise -- 3.6 players per season who have also been Mets. The franchise with the lowest percentage is the Twins, with only 58 players who also played for the Mets at some point.
I offer the neologisms "multijugular", for players who play for multiple teams over their careers, and "unijugular" for the opposite. Jugular comes from the Latin word for yoke, especially in the context of yoking oxen together in a team, and is the basis for English words related to bringing things together, such as join, joint, conjugal, and subjugate.