It appears, according to 11.01 of the by-laws, that there's a suspension option available to the conference as regards West Virginia. Since they've attempted to withdraw, and the lawsuit they have filed should constitute an attempt to withdraw without following the provisions in 11.02, a 3/4 majority vote of the conference board (once WVU has had their chance to explain in front of the board) can suspend West Virginia from conference play in any sport (and for fewer than all sports, that is 3/4 of the membership who plays in that sport - for football, that would be 4 of the 5 schools remaining; for basketball, the threshold is ten members). The board can also vote to terminate, but that gives WVU exactly what it wants.
So it appears that, should the Big East need an option beyond the countersuit, that it can suspend West Virginia in football and basketball, which means they derive no NCAA tournament, football bowl, or television revenue in those sports. It's unclear, however, as to what the other rights of membership are that WVU can be denied (and very possible that it's written into the terms under which the school would be suspended).
Of further interest is that the suspension is not subject to an outside review or appeal, and can only be overturned by a 3/4 vote of membership.
I wouldn't expect a suspension to happen, though, unless (a) the two suits aren't merged into one action, (b) the suits are not somehow settled out of court, and (c) WVU's suit is denied and the Big East's is upheld, meaning WVU will be held to the full exit provisions, including the 27 months. At that point, the purpose would only be punitive (and probably seen as petty, which is probably why, as far as we know, it hasn't been pursued yet).