What franchise1 had the most concurrently2 airing American3 television shows?
Additionally, I was disappointed to find out that both those franchises only managed to do so with one of their shows being just a single short season (Law & Order: Trial by Jury and Chicago Justice). So as a follow-up, has any franchise managed 4 or more where each of the shows involved were successful enough to run more than one season?
I'm willing to accept a loose definition for "franchise", but the occasional cross-over isn't enough.
By concurrent, I mean each show's airing schedule is more or less independent from the others.
I'm restricting to American because it's what I'm more familiar with and I suspect the history and standards of each country's tv industry make cross-country comparisons not very meaningful.