Dayyyyyuuummmmmmm...
Did Ryan24 go on a "Delete-athon", or what...?!?!! Duuuuude...
Really...?Anyways...

In short, the "team" can do what they want, up to "4 games" in terms of "in-house" punishment. Any over that has to go through GODells office in New York.
From...
http://cowboysblog.dallasnews.com/2012/07/daryl-johnston-suspending-dez-bryant-may-be-only-option-for-cowboys.html/?fb_comment_id=fbc_10150929474390303_22922636_10150930240810303#f30635d26c0c59aAnd this is regardings Dez's lattest predicament...
Under the guidelines of the NFL’s personal conduct policy, Bryant could be suspended up to four weeks without pay for “conduct detrimental to the club.”
So ummmmmm, yeah... The "team" can do what they want to... "in house", and anything above and beyond 4 games goes before the Commish.
Not to say they can't appeal the decision, but... We're talking about filing an appeal with GODell.