What's the best three movie run within a franchise not starting with the first film?

So I just rewatched Star Trek 3 The Search for Spock, which I find to be the most underrated Star Trek film. This is particularly impressive given the most compelling original cast character is barely or arguably not in it at all.

I also find that run of Wrath of Kahn, Search for Spock, and Voyage Home to be among the best three movie runs within a franchise that don't start with the first movie.

Usually the fist movie of the franchise is good enough to get a franchise going and usually franchises tend to go downhill fast after the third film, so the original cast Star Trek movies are one of the few exceptions as far as I can tell.

I can think of a horror franchise and an action franchise that both apply to this topic.

Thoughts?

To Download Latest Movies - CLICK HERE