Hal: Mets fall of '69, Knicks spring of '70; also Lakers and Dodgers in '88. In baseball-football, Yankees/Giants did it in '38 and '56. I immediately guessed 'Knicks-Yankees', just because the Yankees have so many titles the odds are good, but forgot that the Knicks only titles came during the '64-'76 Yanks malaise. Oddly, the most recent (football) Giants titles came during Yankees droughts as well (the '81-'96 drought and '01-present). Rangers-Yankees also have some overlap, I think. No three-fers for NY that I can see, and I can't imagine there are any for other cities either- Chicago's baseball titles well predate professional football and basketball; the Lions and Tigers had long dry spells, and so on. It'd be interesting for someone with more time on their hands to see if the three appearances in championship games in the same year is unprecedented- I'd imagine it must be. (Handy reference chart for someone who wants to undertake it.)
So now I've got a spreadsheet (no losers, only winners. Someone else can do that.) I think I've got the years lined up right, though I probably don't account for things crossing years very well (like Sox '07/Celts '08 if it happens.) Besides the ones mentioned above: '35: Detroit Tigers/Lions, and Red Wings won in spring '36, so I guess all three teams were holding the title at the same time? '27: Yankees/football Giants, though the Giants did not win a championship game- merely had the best regular season title before there was a championship game. '28: Yankees/Rangers '33: baseball giants/Rangers '52: Lions/Red Wings (I ignored the AFL-NFL split years in the '60s for football; also, during this period the Lakers were losing a lot to the Celts while the Dodgers were winning.) Impressively, the Celts and Bruins managed to miss each other in the late '60s/early 70s, looks like. Ditto Pirates/Steelers of the same era. '86: Mets/football Giants '89: (sort of): A's/49ers (obviously giants/raiders fans disagree.) '04: Sox/Patriots (duh, given how this came up.) Perhaps the thing that was most interesting to me about this list was how many great dynasties (Jordan's Bulls, the Yankees, early Celtics, '49ers, Steelers, etc.) never overlapped with other great teams in their cities. You'd think that would happen more often. Boston fans really do have it historically good in that sense- even Detroit in '35/'36 didn't have that.
You forgot the '02 Angels and Lakers...
You forgot the '02 Angels and Lakers... and... the Mighty Ducks lost game 7 of the 2002-2003 Stanley Cup Finals against Detroit.
The Mighty Ducks lost game seven of the 2002-2003 Stanley Cup Finals against New Jersey.
touche!
My list had the Angels listed as the Anaheim Angels so my brain skipped over them.
I guess it's different for LA since it could be any combination of the Angels/Dodgers, Lakers/Clippers(ha ha), Ducks/Kings...