This idea struck my mind a few months ago, with how they are re-making a lot of old shows under the "Same Name" of the original.
Gimme A Break! would not work. Nell is gone. It would be very dumb to re-make the show and tie it into the original in some way, as pretty much a lot of the re-makes are doing, unless they just re-made the show under the same name and didn't associate it with anyone from the original cast, but then it would also be just as dumb to re-make.
The only show I could see working is Full House, even if it's under the same name, and even if they brought everyone back, but John Stamos said he wouldn't do a reunion, so it would be weird if they ever re-made the series 15+ years later.