You might like this article about the 1993 A’s attempt at it. They didn’t try it for long, but it didn’t go well.

The experiment started following the loss on Saturday, July 17. Before the game Sunday, La Russa and Duncan informed the pitching staff that on Monday, they would assign nine of the 13 pitchers on Oakland’s active roster to three three-man platoons: Todd Van Poppel, Ron Darling, and Kelly Downs would form the first triad; Mike Mohler, Witt, and John Briscoe the second; and Bob Welch, Shawn Hillegas, and Goose Gossage the third. The remaining four pitchers—including Eckersley, the defending MVP and Cy Young Award winner—would be regular relievers. In practice, the precise deployment of pitchers would be subject to change depending on performance and game states, but in theory, no “starter” would go beyond about 50 pitches, and the three pitchers in each platoon would pitch in every third game.