It's going to be difficult. The ACC/B10 challenge is such a unique beast. Outside of that, the best thing that they can do is get the marquee television draws from the league matched up with top level opponents. Maybe not a conference challenge, but perhaps some good match ups between BE and Pac 12 teams would be nice.
PAC 12 has done a conference challenge series with Big 12 in the past, so I'd hope that they would be open to one with the Big East. We both have TV partnerships with Fox. Marquette has not had much luck out west, but I'd love to play Zona again, UCLA, Oregon, etc.
Big 12 has one with the SEC now, don't they? Seems like that would open the Pac-12 up for an East vs West challenge. Could be fun, and having both conferences affiliated with Fox Sports would make things easier, I'd imagine.