There have actually been 4 different players that have played with 36 Hall of Famers
Joe Bush - Baker, Bender, Carey, Cobb, Cochrane, Collins, Combs, Coveleski, Cronin, Cuyler, Foxx, Gehrig, Goslin, Grimes, Grove, Harris, Hooper, Hornsby, Hoyt, Jackson, Johnson, Lajoie, Lindstrom, Ott, Pennock, Plank, Rice, Roush, Ruth, Sisler, Simmons, Speaker, Terry, Traynor, L.Waner, P.Waner
Doc Farrell - Bancroft, Bottomley, Combs, Cronin, Cuyler, Dean, Dickey, Evers, Ferrell, Frisch, Gehrig, Gomez, Grimes, Grove, Hafey, Haines, Hartnett, Hornsby, Hubbell, Jackson, Kelly, Lazzeri, Lindstrom, Maranville, Ott, Pennock, Roush, Ruffing, Ruth, Schalk, Sewell, Sisler, Southworth, Terry, Wilson, Youngs
Burleigh Grimes - Bottomley, Carey, Combs, Cuyler, Dean, Dickey, Durocher, Frisch, Gehrig, Gomez, Hafey, Haines, Hartnett, Herman, Hornsby, Hoyt, Jackson, Kelly, Lazzeri, Lindstrom, maranville, Marquard, Medwick, Ott, Roush, Ruffing, Ruth, Sisler, Terry, Traynor, Vance, Vaughan, Wagner, L.Waner, P.Waner, Wheat
Waite Hoyt - Baker, Cochrane, Combs, Coveleski, Cuyler, Dickey, Durocher, Foxx, Gehringer, Gehrig, Gomez, Grennberg, Grimes, Grove, Harris, Hooper, Hubbell, Jackson, Kelly, Lazzeri, Lindstrom, Lopez, Manush, Ott, Pennock, Ruffing, Ruth, Simmons, Terry, Traynor, Vance, L.Waner, P.Waner, Wilson, Youngs.
edit: Next on the list is:
Bobo Newsom 32
Leo Durocher 30
Bob O'Farrell 30
Surprisingly, Yogi is tied for 1625th place with 9. I thought he'd be higher myself.