Okay.

1. Brando starred in Julius Caesar (1953) with John Hoyt and Michael Ansara.
2. Hoyt and Ansara both guest-starred on TOS.

Most of the classic stars are just one or two degrees from Shatner. Let's try Yvette Mimieux.

Marlon Brando.

1.Marlon Brando starred in "The Men"1950 . Deforest Kelley also starred in the same film.

Charlton Heston

Charlton Heston

1. Chuck starred in Soylent Green with Celia Lovsky, Roy Jenson, and Whit Bissell.
2. Jenson, Bissell, and Ms, Lovsky all guest-starred on TOS.

Yvette Mimieux?

Yvette Mimieux starred in 'Joy in the Morning.' Richard Chamberlain starred in the same film. Richard Chamberlain was the main character in Dr. Kildare . Leonard Nimoy starred in an episode of the series.

Charlton Heston.

Also

Charlton Heston starred in ' The Ten Commandments' Yul Brynner starred in the same film. Yul Brynner starred in Catlow. Nimoy played also in Catlow.

Well done jxh13 ! Leave it to you to write the next actor.

Lana Turner

@sunshine62 said:

Lana Turner

1. Lana Turner starred in the movie "Latin Lovers (1953)" with Ricardo Montalban.

2. Ricardo Montalban played Khan Noonien Singh in the STOS and the movie "Star Trek II: The Wrath of Khan (1982)" with Shatner, Nimoy and DeForest Kelley.

Nancy Guild

1.Nancy Guild and Orson Wells in 'Black Magic.'

2.Orson Wells and Richard Basehart in 'Moby Dick.'

3.Richard Basehart and William Shatner in 'Brothers Karamazov.'

Robert Wagner

Robert Wagner

1. Robert Wagner played Jesse James in "The True Story of Jesse James," co-starring Jeff Hunter, Frank Overton, and Frank Gorshin.
2. Overton & Gorshin guest-starred on TOS, while Hunter appeared in the Pilot, "The Cage," with Leonard Nimoy.

Ringo Starr?

1.Ringo Starr and Richard Burton in Candy .

2.Richard Burton and Joan Collins in Sea Wife. Joan Collins starred in The City On the Edge of Forever.

John Wayne

John Wayne

1. The Duke starred in 'True Grit' with Kim Darby, John Fiedler, and Jeff Corey.
2. Miss Darby, Fiedler, and Corey all guest-starred on TOS.

Keanu Reeves?

Also .. 1.John Wayne and Richard Widmark in Alamo.

2.Richard Widmark and Deforest in Warlock.

Keanu Reeves?

1.Keanu Reeves and Charles Bronson in Act of Vengeance.

2.Charles Bronson and Yul Brynner in The Magnificent Seven.

1. Yul Brynner and Majel Barrett in WestWorld .

Majel Barrett -Nurse Chapel

Burt Lancaster

Burt Lancaster

1. Burt appeared in "Gunfight at the O.K. Corral" as Wyatt Earp; De Kelley played his brother, Morgan.

Steve Reeves?

Steve Reeves?

This one is hard. I am sure there is a shorter route, but I am sticking with movies I have actually seen.

1. Steve Reeves starred in The Thief of Baghdad (1961). Arturo Dominici played Prince Osman in that movie.
2. Arturo Dominici appeared the low budget horror film Black Sunday (1960). John Richardson was the male lead in that film.
3. John Richardson was also the male lead in One Million Years B.C (1966). Few people noticed him because bikini clad Raquel Welch dominated the screen, stealing scenes even from the Harryhausen dinosaurs. (When I was in third grade, though, the dinosaurs were the real stars.)
4. Raquel Welch was in several movies that featured Star Trek guest stars. The very first one I saw was 100 Rifles. (My dad made me cover my eyes when she showered under a water tower. Michael Forest, who plays Apollo, is in that movie. I didn't notice him until I watched it again unchaperoned years later.

Groucho Marx?

(Edit. I just remembered a very short path involving Groucho. I'm sure others can do the same.) (Edit 2. &$#*!!! I just noticed that I am supposed to link to Shatner, Nimoy, or Kelley. I guess that means we need one more step. If a judge declares this post to be invalid, I would completely understand.)