Director John Ford had a “stock company” of actors (including John Wayne). Some probably appeared together in 10+ films. Probably the largest number would be the combination of Harry Carey and John Wayne, though Carey and Francis Ford may have more.
Fredric March appeared with his wife Florence Eldridge a number of times on stage and screen, such as “Inherit the Wind”. I don’t know how many.
Bruce Willis and Samuel L. Jackson have been in at least two together: Die Hard 3 and Unbreakable.
Besides the “Road to” pictures, of which there are seven, Bob Hope and Bing Crosby would occasionally have cameos in each other pictures. One example is “The Princess and the Pirate” when at the end Virginia exclaims how happy she is to be reunited with her hero and runs past Hope who thinks it’s him she wants, into the arms of a sailor played by Crosby.
Nowhere near the top, but…
Humphrey Bogart and Bette Davis were in 7 movies together.
- Pulp Fiction
What happened to the “3 stars” and “significant roles” parts of the question?
Heath Ledger, Mark Addy and Shannyn Sossamon had the three starring roles in both The Order and A Knight’s Tale. These were so unrelated they weren’t even set in the same century, though both were written and directed by Brian Helgeland so it wasn’t exactly coincidental.
Richard Burton and Elizabeth Taylor did 8 films together:
Cleopatra
The Taming of the Shrew
Who’s afraid of Virgina Wolf
The Comedians
The Sandpiper
The V.I.P.s
Divorce His - Divorce Hers
Boom!
Moe Howard made something like 200 shorts with Larry Fine.
Does Helena Bonham Carter do anything without Johnny Depp anymore?
John Cleese and Jamie Lee Curtis were both in “A Fish Called Wanda” and “Fierce Creatures”. Along with about a dozen other people! Only two movies but a lot of the same people. Much like John Ford’s trusted players.
Abbott and Costello were in about 40 movies together, and I think only a couple of them were related to each other.
Thought of another three-fer:
Michael Douglas, Kathleen Turner and Danny Devito were the three main characters in both Romancing the Stone and War of the Roses.
Well, there is the lucrative Harry Potter franchise…
And The King’s Speech.
I think a lot would depend on how you define unrelated plot.
You’sd need to consider the Sherlock Holmes movies (Holmes and Watson), Charlie Chan, Bulldog Drummond- that sort of genre.
The plot of each may be unrelated to a previous movie but the theme is the same.
Forget Cleese and Curtis - those movies also have Cleese and Michael Palin. Their shared filmography includes:
And Now for Something Completely Different
Monty Python and the Holy Grail
Life of Brian
Time Bandits
The Meaning of Life
Fierce Creatures
Absolutely Anything
Still only seven, though, so small change compared to some of the other suggestions.
Woody Allen & Diane Keaton did six movies together:
Sleeper
Love and Death
Annie Hall
Interiors
Manhattan
Manhattan Murder Mystery
Then Woody & Mia Farrow did nine movies together:
A Midsummer Sex Comedy
Broadway Danny Rose
the Purple Rose of Cairo
Hannah and Her Sisters
New York Stories: Oedipus Wrecks
Crimes and Misdemeanors
Alice
Shadows and Fog (TV movie)
Husbands and Wives
Judy Garland & Mickey Rooney…
Clint Eastwood, Sandra Locke, and Geoffrey Lewis were all three in Bronco Billy, Every Which Way But Loose, and its sequel Any Which Way You Can.
Locke and Eastwood also starred together in The Gauntlet and The Outlaw Josey Wales.