Right now the chess.com tournaments are subdivided by rating which makes sense and has its place.  Would it be possible to have every 3rd or 4th iteration an open one?  Set up and run it like a Swiss or a direct elimination.  I realize the Swiss version would take some time to go through 4-6 rounds or more might it might be worth the effort.

Different type of tournaments would be fun to. An eimination tournament (maybe 16 to a field (NCAA style) would be cool 2. 

A Swiss would take forever! The 2nd round could only start when ALL the games in the 1st round were finished - that takes what, five months? And if you only have 4-6 rounds with 1000 players, a lot of people are going to end up joint #1; you need many more rounds to decide who is the best.

Pretty much the same goes for elimination.

you can already setup a bracket-like elimination - just make group size of 2 :)

I know it would take a long time, that's why I suggested infrequent scheduling.  Patience is a virtue.

Can approximate this as indicated by erik.

But ... with 2-player groups there are many ties. It is almost automatic there will be an extra round.

16 players: extra round and another with an extra round.

16 players with three withdrawals: no extra rounds. 

4 players: three extra rounds.

If such a format was offered the maximum limit could be set to a reasonable number. No official unlimited tournaments.

Don't forget most Swisses end in tie breaks. Even Round Robins do as well.  There is no need to extend to 10/12 rounds hoping someone ends up alone at the top.