One concern being floated out there (for quite some time, actually) is that the Big East can't afford to add any more basketball teams should they decide to expand. The usual football/basketball split is often mentioned to alleviate some perceived notion that more than 17 basketball teams couldn't/shouldn't happen.
I previously wrote in one of the expansion pieces that adding more basketball teams shouldn't be an issue. The big thing with keeping the number of teams down is so that you can play each team at home and on the road - that already doesn't happen in the Big East. Instead of playing three opponents home/away, if the conference moved to 20, you could simply play every team once and alternate location each year.
Now, with more expansion talk about adding Kansas, Kansas State, and Missouri, there's another option being floated out there as far as how to handle 20 teams.The New York Post says there could be four five-team divisions instead. Each team would play a home/away with teams in their own division and then play against other teams on a semi-annual basis.
Frankly, I like my idea better. I'd much rather play every team in the league. In the idea mentioned in the Post article, eight games would be tied into your four other division members. Keeping the current 18 conference games, that means you'd get to play an additional ten teams, leaving a total of five that you don't play in any given season. Pitt has nice rivalries with teams like UConn, Syracuse, and West Virginia. To a slightly lesser extent, Villanova and Georgetown are also teams to look forward to. I'd hate to see a couple of those teams not on Pitt's schedule every few years.
Either way, though, 20 basketball teams in one conference is definitely possible.