Could they sue? Sure — they’ve done it before. Should they? Probably not. An lawsuit might help negotiate a mitigated settlement or shave penalties, but proving damages would be exceedingly difficult, and there’s no injunctive relief left worth the cost of litigating (no obvious hair-on-fire hook to obtain quick court intervention).
Despite being a “repeat and aggravated Level I violator,” Michigan avoided a postseason ban. Without a postseason ban or other drastic enforcement action, courts are unlikely to intervene, much less enjoin. They generally defer to NCAA autonomy on discipline (unlike NIL compensation or athlete-rights policy, which they’re all to eager to jump right into).
Plus, Michigan’s own failure to cooperate in the investigation severely weakens its own case, and fighting over its own wrongdoing risks backfiring with regulators, the media, and the public. A less adversarial route — appealing directly to the NCAA — might have a better chance at reducing penalties or securing relief.