Leeds forwards Jamie Jones-Buchanan and Nathaniel Peteru face lengthy periods on the treatment table.
Jones-Buchanan will have a clear out operation on his knee and will be out for six to eight weeks.
Prop Peteru will be out of action for 10 to 12 weeks with a bicep tendon rupture in the other arm from where he suffered a similar injury earlier this season.
The news comes just a day after the Rhinos found out captain Kallum Watkins was ruled out for the rest of the season with an ACL injury.
Six more players are doubtful for Leeds’ clash with Catalans Dragons on Saturday, with Joel Moon, Carl Ablett, Matt Parcell, Stevie Ward, Brett Delaney and Jack Walker all being assessed further this week.
Richie Myler will see a specialist before being given clearance to return to play after his concussion assessment during the Rhinos’ Magic Weekend defeat to Castleford Tigers.
The Rhinos will also be without Liam Sutcliffe, Mitch Garbutt, Brad Singleton and Anthony Mullally in Perpignan.