If they're not interested in promotion and relegation maybe a national cup competition, like the FA Cup in England, could be one fun way to have some level of integration with the other levels. The excitement of cup competitions would boost attendance across the board, and fun moments like cup upsets (a lower tier team defeating a top-tier one) raise the profile of the sport overall through media exposure.

It's maybe more tempting for MLS to focus on money-spinning continental competitions like the CONCACAF equivalent to the Champions League. But I think they'd be missing out if they didn't at least explore a "US FA Cup" as a means of growing interest in the domestic game itself, which indirectly benefits them.