Kirk Broadfoot faces a three match ban after his red card against Aberdeen.
Should the appeal fail, he will miss Celtic (away), Hearts (away) and Hibernian (home) and would be back in contention for the final game of the season against his former side Rangers.
His red card against Celtic in February means that he will be suspended for an extra game on top his immediate two.
The club will also appeal Rory McKenzie's red card, and he faces a two game ban should it fail (Celtic and Hearts).
Stuart Findlay will be banned for one game (Celtic) after his two yellows.
Speaking on the reds, Steve Clarke said: "I thought Broadfoot's was a genuine attempt to play the ball.
"There was no malice, no violent intent. It was two brave players going for the ball.
"Kirk's foot hit the top of the ball which made it look worse than it was, we will appeal that.
"Stuart had two yellows and I've got no complaints over that.
"Rory's the referee wasn't looking at it, so I can only assume the decision came from the fourth official who was standing next to me and he couldn't see it.
"After seeing it back on video it was almost nothing so we will appeal that too."
