You can challenge any goal for offsides or goalie interference but you can't challenge any play for too many men? That makes so much sense. You should be able to challenge any play at any time for too many men, illegal equipment, kicking or batting the puck in goal, goalie interference, and puck out of play. Those all should be apparent to the War Room as well but we won't get into the sticking points of when Toronto can and should get involved in reviewing plays when the on-ice officials have that same ability.
And get rid of the offsides review all together - it's stupid. Go to a system of max 2 challenges for any of the above where if you win the first challenge you keep your timeout and challenge a 2nd time. No penalty if wrong, just you lose your timeout and can't challenge a 2nd time. Teams shouldn't be punished for fixing an officiating wrong by losing the timeout or the ability to fix a 2nd mistake also later in the game. It's screwy that getting something corrected has a negative impact to you after the fact.