You can appeal to the entire 2nd circuit court of appeals. That's called appeal "en banc". Then all of the judges of the 2nd circuit (usually around 10 or so for most circuits) would review the case and issue a ruling instead of just these three.
En banc appeals are almost never allowed.
The other avenue is SCOTUS.
SCOTUS appeals are like 1% heard, and there is nothing in this case so special (in terms of the law) that would suggest for a second that the Supreme Court should hear it. They don't hear cases just because someone famous is involved.
So this is it for Brady, pretty much. Case closed. BB has 4 months to get Garroppollo ready for the first four games. Knowing him, Garappollo plays well, gets benched after four games, Brady plays like his hair is on fire, the Pats win the SB, and Garapalo (can you tell I don't know how to spell his name) gets traded for a first round pick.
And then the Pats haters cry again about how unfair the world is.