Can that happen? I know if a court ruling is appealed, the appeals court can change the compensation/sentence up or down if they feel the previous ruling was too lenient/harsh. If the NHL points to the Perron suspension and says he should have got 6 games but shaved 1 off due to not having a history, can the arbiter tack on the extra game?
Also, I don't understand what Rielly's defence could be. "He did something that made me angry so I crosschecked him in the face" isn't much of a justification for appeal.
His defense will likely be
A. his stick rode up, it wasn't his intent to hit him in the head
B. No prior history
C. Other suspensions were shorter.
The first two were already addressed in the initial ruling, Bettman may chose to agree or disagree with how much of an impact they deserve when considering the length but nothing new here. The third was tried by Perron and Bettman already brushed it off as in compelling.
I doubt the appeal goes anywhere, it seems more about pageantry than realistically expecting a positive outcome, though I suppose you might as well challenge and get your money's worth out of union dues, not like Rielly has to do anything aside from say, yes, please appeal on my behalf while I sit at home and binge Netflix with Tessa.