Not if you want people to be able to watch you without going into buffering hell. That's the reason to limit it to 2000kbps; Twitch released usage metrics, and that's the point where the widest audience will be able to watch smoothly. Even bumping to 2500 will cause a significant portion of viewers to start having issues. 60fps is mostly numbers-wanking anyway, when it comes to streaming (as opposed to playing) without a technical need (like if a game uses sprite blitting for transparency, causing items to disappear or stay solid when streamed at 30fps).
A better idea is to step to a slower x264 preset. Start at Veryfast, and monitor your CPU load and temperatures while streaming and playing your game of choice. After about 20 minutes, move one step slower on the preset list, and test again.
Slower preset = better compression = your stream will look better at a given bitrate. But more CPU is used.
Your bottleneck is your viewers' connection to the Twitch server. Not your hardware, or anything you can control.