re: Last time your school held 2 of the big 3 sports championships at the same time?

aTm has never been close in the Big 3.

Near term going forward Men's only chance is Football (obviously) and Baseball (hot pitching at the right time always makes it possible aka see recent Cock titles). If you add women in the mix then WBB has a dark horse possibility and the hot pitcher applies to softball as well so their is also a dark horse chance.

Historically:

Football has only sniffed a title a couple of times since 1940
MBB has historically been a dumpster fire.
WBB won one two years ago
Baseball has been to a couple of CWS's but never made it to the final
Softball was in the final a couple of years ago and won it all in 82 (AWIW which preceded the NCAA for women), 83 (NCAA), and 87 (NCAA).

Right now I would take two of the three Big 3 in the same decade.

Outside of the big 3 aTm best year was 2009 when 4 titles were won: MOT, WOT, M-Golf, W-Western Equestrian

Most dominat have been Men and Women's both winning 3 Outdoor Track titles in 09, 10, and 11

Women's Equestrian has won some sort of Equestrian title each year from 02 through 12 except 06, 08, and 11. Of course none are NCAA since Equestrian has been governed by bodies such as the Intercollegiate HSA. And unless you are an UGA and aTm fan then it is highly unlikely that you care and even if you are it is still unlikely.