It was sometimes known for guys to serve one family as an associate before being passed on to another where they were subsquently made.
For example, Sammy Gravano, Gerrard Pappa and "Donnie Brasco" all began mob life with the Colombos but ended up with the Gambinos, Genovese and Bonnano's respectively (Brasco was on the brink of being made before his real ID was revealed).

Brasco moved of his own accord (Mirra and Lefty were juicer targets than any of Jilly Grecas crew).
Gravano shifted because he fell out with Shorty Spero's brother and the Colombo hierachy didnt want any future problems.
I dont know why Pappa moved to the Genovese? (perhaps the Colombo's were sick of him? - LOL)

Anyway, all the above men were not made when they had their mob transfers - did any men ever move to a different family AFTER they were made?