Hmmm...
More silly interactions. Some of Richard Dean Anderson's lines in the SG1 series really cracked me up at times, as well as how irreverantly they treated the material at times.
I'm specifically thinking of an episode where SG1 gets captured (again), and O'Neal is cracking wise as usual...
Jonas: So what now?
Teal'c: We wait.
Jonas: Shouldn't we be trying to escape?
O'Neill: Oddly? No. Won't be long.
Jonas: Before what?
O'Neill: Oh, some overdressed, over-the-top bad guy floats in, gloating about whatever evil fate awaits us. ... Wait for it. {The door opens}. See?
Other than that, well the ship thing has been done (Universe), the Colony/Station thing (Atlantis), and the first contact team thing was done to death in SG1. The ever escalating bad guys syndrome persists in this series: in Star Trek, Klingons gave way to more grouchy Romulans, who were supplanted by the Borg... In SG1, the Replicators were scarier than the Goa'uld, then they brought in Anubis as a bigger and better Goa'uld, then those guys weren't tough enough so the Ori appeared...
Maybe a 'brave new world' thing, where Stargate Command is establishing a colony/base somewhere that ISN'T cut off, but the world holds many secrets? And other races/powers also are interested, and are setting up colonies of their own on this world? Maybe...
A whole new direction would be nice, one where the Stargates are used occasionally perhaps?
I'm guessing that SGU is the death knell of the Stargate franchise, though, seeing it was cancelled. And the movies, while interesting, aren't going to resurrect the series.
I'm a huge fan of the Asgard, too bad they were killed off...
Definitely an interesting thought problem, seeing there are 17 seasons or so of Stargate shows in the bag currently...
Sirgod's idea has some merit I think.