3 guns (rifles, shotguns, pistols, etc) in 1 case is no problem as long as the case meets the TSA requirements of hard sided and fully locking so that the guns cannot be accessed without opening the locks first.
Thanks! I ended up only taking 2. At some point my gun case locking part broke - one "eye" had no idea until checking in at Jackson Hole. TSA let it go even though they could pry it apart. I got LUCKY.