The Scottish Football Association have offered two-match suspensions to St Mirren midfielder Jim Goodwin, Motherwell midfielder Steve Jennings and Aberdeen midfielder Peter Pawlett.
Goodwin and Jennings were involved in an altercation during the 1-1 Scottish Premier League clash at Fir Park on Saturday.
Television pictures appeared to show a punch from Goodwin into the stomach of Jennings following a foul by the English midfielder.
Both players were booked by referee Calum Murray following the incident but could face further punishment after notices of complaint were issued by the SFA's compliance officer.
Pawlett has been accused of simulation to win a controversial penalty during the 1-0 win over Hibernian at Pittodrie.
The Scotland under 21 player fell theatrically inside the box as Hibs winger Ivan Sproule chased back for a loose ball and referee Craig Thomson awarded a penalty, which was converted by Scott Vernon.
The SFA's compliance officer has previously offered Garry O'Connor and Rangers winger Sone Aluko two-match suspensions for simulation following controversial penalties, although the former escaped punishment after a hearing.
Clubs have until 3pm on Wednesday to respond to any notices of complaint.
On Monday, Aberdeen confirmed that they have appealed against the red card shown to Pawlett later in the game against Hibs, after sliding in as Lewis Stevenson made a clearance.
Pawlett's appeal against his red card will be dealt with by a Fast Track Tribunal on Thursday.
Dundee's Stephen O'Donnell, who appealed against the red card he picked up against Ross County at the weekend for a challenge on Iain Vigurs, will also have his case heard.
Should Pawlett, Goodwin or Jennings choose to refuse the offer of their two-game bans, then it will be referred to the Judicial Panel and a Fast Track Tribunal will be convened, also on Thursday.