We have 27 rounds in our draft.
We have an 8 man minor league system. They roll over indefinitely as long as they still qualify as "rookies" (so Cameron Maybin, for instance still can stay on someone's minor league system). However, to put someone on your minor league roster, they can't have ever played in the majors (so nobody could pick up Pablo Sandoval for their minor league roster even though he technically qualifies.
I know that's not your question, but minor leaguers and free agents are the only two types of players which fall out of the "round + 3" rules.
If you want to keep one of your minor leaguers who lost rookie eligibility (like Jay Bruce), they cost a 27th round pick (this may sound like it's too much of a difference maker - but I've had Jay Bruce on my team since 2007)
If you want to keep a free agent, you have to give up a 15th round pick. There were some that wanted no free agent pickups to be kept at all (which I kind of liked - this would benefit people who had good drafts), but we settled on the 15th round.