You can do some "non bridge" palm muting with your picking hand. It requires a light technique in order to keep it from giving you totally muted notes. Just don't push down with the palm of your hand. Just set it there lightly. Being able to mix non muted, lightly muted, and heavily muted sounds can offer a lot of dynamics to your playing.
Give it a try and see what you think.
Carvin Club #167
Switch-Hitter #25 (musical switch-hitter you pervs! Musical!)