Philly has come close.
Flyers - 1975
Phillies - 1980
76ers - 1983
but the Eagles couldn't win the Super Bowl in Jan. 1981
Philly even had a chance for all four franchises to within 12 months of each other, but only the Phillies came through. Given Philly's luck, it's amazing that even the Phillies won!
76ers - spring 1980 (lost in finals)
Flyers - spring 1980 (lost in finals)
Phillies - 1980 (won world series)
Eagles - 1980 - 81 (lost Super Bowl in Jan 1981)