Larry Sabato advocates something like this. The President serves for 5 years, then decides whether he wants to pursue an extension. If no, then the term ends at 6 years and a new presidential election is held with new candidates. If yes, then the nation votes on an extension referendum. Should the nation vote to grant the extension, the President serves another 3 years, making one total 8-year term. If the nation votes against granting the extension, the President serves only 6 years, and a new presidential lection is held.
The policy behind it is to give the administration time to work before entering re-election mode.
Hmmm, I wonder how that would've worked with Bush. There is no way he would've gotten an extension.