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Manchester City have written to the body responsible for professional referees following a number of bad tackles on their players, Press Association Sport has reported.
Premier League leaders City have reported nine challenges they feel were not sufficiently punished by referees in recent months to Professional Game Match Officials Limited (PGMOL).
City would also like to see a change in Football Association rules that would allow incidents seen by referees on the field to be reviewed again retrospectively.
That could possibly mean yellow cards being upgraded to red if evidence was sufficient.
City's move backs up repeated calls by manager Pep Guardiola for players to be given better protection.
They see it as something that could benefit the whole of the game and believe other clubs might support it.
In one of the worst challenges, a fortnight ago, winger Leroy Sane suffered ankle ligament damage after being caught late by Cardiff's Joe Bennett in an FA Cup tie.
Bennett received only a yellow card, as did West Brom's Matt Phillips for a high tackle on Brahim Diaz three days later.
Other bad challenges to have sparked controversy include two on Kevin De Bruyne by Crystal Palace's Jason Puncheon and Tottenham's Dele Alli. De Bruyne was also the target of a cynical foul attempt by West Brom's James McClean.
Spurs' Harry Kane also caught Raheem Sterling and challenges on Ilkay Gundogan by Claudio Yacob of West Brom and Newcastle's Jacob Murphy caused concern.
Youngster Phil Foden suffered ankle ligament damage after a challenge by Leicester's Harry Maguire.
Last month, Guardiola said he had no plans to call for a meeting with Mike Riley, the head of PGMOL, but City now feel strongly on the matter and hope their letter can prompt a conversation.