As many of you may know, in the Arrowerse we had episode starting in Arrow then continuing on The Flash then on Batwoman, and on Supergirl. I don't think that is the reason they may be part of the same franchise, but I wonder if that alone would be reason enough?
The reason I'm asking is because "Magnum, P.I." and "Murder, She Wrote" had similar crossover.
The episode started with Magnum episode... https://www.tvmaze.com/episodes/92984/magnum-pi-7x09-novel-connection
...and then continued on Murder, She Wrote... https://www.tvmaze.com/episodes/164965/murder-she-wrote-3x08-magnum-on-ice
Now, apart from that I don't think they ever crossed over those characters. Though there are similarities seeing how they both solve various crimes, Magnum being paid for it since he's a private eye, and Jessica doing it on her own as a hobby, since she is a crime novel writer.
So, my question is, since those two main characters crossed over to each other's tv series, does that make the two series part of the same franchise?