The more I think about it, the third movie lost a lot of potential for being a gimmick film. To me, an ideal third film would have been something like this...
Chipmunks 3: Alvin's World Tour.
Dave, and the record label have put together a huge concert tour around the world, which inflates Alvin's ego, only to be deflated when the first country they go to hasn't even heard of them, and only American Tourists and fans are in the audience (Mimicking a scene from Maids in Japan). Alvin is so upset by this, he questions why they left Ian for Dave, also bringing up that they live very modestly for celebrities, and complaining that Dave puts all the money they make into trust funds they can't touch until they're older. Theodore points out that Dave cares about them (going as far to say that trust funds are for if they ever get sick of being in a band and want to do other things with their lives), Simon pointing out "You do remember he put us in a cage, right?" (and then subsequently bringing up the word "cage" everytime Alvin complains)...
After a small fight, Alvin decides they should hire a better public relations/press agent (Dave doing it himself beforehand), Dave doesn't like the idea at all, Alvin goes behind his back and hires one. The group's publicity shoots through the roof, and every other concert tour is packed with foreign fans. Meanwhile, the Chipettes are sick of opening for the Chipmunks and living in their shadow, and Brittney hires the very same press agent behind the backs of Dave and Alvin (actually, not knowing it is the same agent) to make them just as famous, if not more than their male counterparts. You see the press agent struggling to hide each group's involvement that culminates in a cliche sitcomish scenario where they have meetings scheduled at the same time.
Of course, the big reveal is that the press agent is actually working for Ian, who's desperate to steal their likenesses and music rights, and has hired him to steal important documents and forge signatures. When this is discovered by Simon and Jeanette (both being the smart ones), Alvin and Brittney refuse to believe it's true, get into a fight for hiring the same agent, and then stumble onto evendence that it was true the entire time.
At the end of the film, Dave steps in and saves the day, showing the press agent that Ian was going to screw him out of the deal anyway and not even paying him for his services. Dave hires him willingly, causing the press agent to destroy the forged documents that would have let Ian have control of both groups. The last concert in the tour is a smash success, the Chipettes prove they're valuable on their own, and everyone's happy. Except for Alvin who keeps pestering Dave to take money out of his trust fund to buy foolish things.
At least, that's how I'D write a Chipmunk movie.