Fox just got their hands on a boatload more basketball games at schools people care about, so I can't imagine the Big East is going to have much leverage.
I posted this elsewhere, but I will post it again because the post explained FOX's need for Big East inventory:
Before I explain who holds various media rights, you need to recognize that the conference networks, BTN, ACCN, and SECN have drastically reduced basketball content as you need to broadcast something of value to maintain carriage.
In the future, FOX owns the media rights for some Big 10 basketball and some Big 12 basketball. Here are what seem to be the commitments (they will probably change slightly with the movement of the Pac 12 teams):
Big 10 basketball games: 126 on BTN, 47 on Peacock, 45 on FOX/FS1, some games on CBS, and the Big 10 Tournament on CBS. (The number of games on FOX are about the same as in the old contract.
Big 12 basketball games: ESPN remains the primary rights holder, but some games will be on FOX/FS1. The number on FOX/FS1 has not been defined as of yet. Championship on ESPN.
ACC and SEC basketball: No games on FOX. Championships on ESPN.
Mountain West basketball games: 45 on CBSSN, 32 on FS1, 2 on CBS, and 1 on FOX. (Runs through 2025/2026, but not really material to the Big East as these are late night games.). Championship on CBS.
Let's now look at the Big East and Pac 12.
Big East basketball games: 120 games on FOX/FS1, 3 on CBS, 19 on CBSSN. The entire Big East basketball tournament is on FS1/FOX.
Pac 12 basketball games: 19 games on FS1, 3 games on FOX. (No contract going forward.). Championship on ESPN.
Overall FOX basketball inventory today is ~223 games with one conference tournament (Big East). Contracted after 2025/2026 ~80 to 90 games per year with no conference tournaments.
One last point. Yormark recognized the flaw in the Big 12's media inventory: he needed more Eastern time zone content for both football and primarily for basketball. (Remember 47% of the country lives in the Eastern time zone.). FS1 has 6:30 PM time slots on weekdays for basketball, but the Big 12 has only 3 Eastern time zone schools. So, the Big 12 does not have enough content for 6:30 PM time slots as you can not start weekday games at 5:30 PM Central time or 4:30 PM Mountain time.
It looks to me that FOX needs the Big East to fill the college basketball content hole.