But good job on Franco; I’d forgotten about him.
I think Errol Flynn and Alan Hale Sr were in nine movies together. Flynn and the indestructible Olivia de Havilland were in eight.
How about Matthew McConaughey and Kate Hudson/
How To Lose A Guy In Ten Days(2003) and Fool’s Gold(2008)
But that post made me look up Abbott and Costello, who made 38 movies together. You could argue they were related, but they had different character names in almost every movie so you could also argue they qualify.
I also wonder if Laurel and Hardy should count. They were in even more films together though many of them were shorts: 34 silent shorts, 45 sound shorts, and 27 feature films.
I don’t think it’s quite in the spirit of the OP. They were comedy partners. Any films they were in together WERE a de facto series. I think the OP is more about actors that just happened to work together multiple times.
Humphrey Bogart and Bette Davis made **Dark Victory **and several other movies together.
Well, lots of directors have stables of actors they like to work with regularly, which means a bunch of those actors will work together a lot.
Woody Allen has often used Diane Keaton, Mia Farrow, Tony Roberts, Diane WIest and Julie Kavner, among others.
Martin Scorsese has brought Robert DeNiro, Harvey Keitel, Joe Pesci, and a few other guys together regularly. Lately, Leonardo Dicaprio has been one of his regulars.
Ingmar Bergman often brought Max Von Sydow and Liv Ullmann together.
Christopher Guest often works with Harry Shearer, Michael McKean, Eugene Levy, Catherine O’Hara, and Jane Lynch.
The Coen Brothers use a lot of the same actors regularly, so the paths of Steve Buscemi, Frances McDormand, John Turturro and John Goodman cross a lot.
Spike Lee uses John Turturro a lot, too- along with Michael Badalucco, Wesley Snipes, Giancarlo Esposito, Samuel L. Jackson, and Denzel Washington.
In a previous era there was the John Ford Stock Company
Right, but Elizabeth Taylor and Richard Burton, Paul Newman and Joanne Woodward, and Spencer Tracy and Katherine Hepburn were all partners as well, though not in the exact same way.
Damon and Affleck were partners.
In some way, many of these duos listed in this thread were partners in some way other than just happening to be in multiple movies together, and that is in fact why they were in multiple movies together.
I actually don’t disagree with you, I’m just pointing out it’s hard to really draw the line.
I think Laurel and Hardy should count only because they bring back memories of us watching them (with movie projector and portable screen) in our living room when I was little. 
But yeah, it is hard to know where the line is. No hard and fast rules here! Fast? No Fast and Furious – definitely a series there!