M3S began on ABC for the 1960-61 season, while CBS' The Twilight Zone entered its second season. By the time My Three Sons moved to CBS for the 1965-66 season, The Twilight Zone had been gone from the network for more than a year. Anyway, just as a fun exercise, let's try to name a lot of actors who made at least one appearance on each series.

Here is my starter list:

Blondell, Joan
Brittany, Morgan (Suzanne Cupito)
Cabot, Sebastian
Cartwright, Veronica
Deacon, Richard
Demarest, William
Francis, Anne
Garland, Beverly
Jackson, Sherry
Macklin, David
Oliver, Susan
Repp, Stafford
Singleton, Doris
White, David

A few additions:

Austin, Pamela
Gould, Sandra
Gregg, Virginia
Gregory, James
Patterson, Hank

Miles, Vera

Gregory Irvin
Terry Burnham
Dana Dillaway
Susan Gordon
Billy Booth

Ann Jillian(n)
J. Pat O'Malley
Nancy Kulp
Raymond Bailey
Roy Roberts
Irene Tedrow
Mary LaRoche
June Dayton
Ned Glass
Hugh Sanders
Edward Platt

Wow! Thanks everyone for the great additions. Looks like it will become a long list.
Edit: Here are 2 more --

Strickland, Amzie
Williams, John

MacMichael, Florence

Willock, Dave

https://www.imdb.com/search/name/?roles=tt0052520,tt0053525&ref_=rlm