I have my hand in a fist shape, with my thumb muting the BEAD strings, and sometimes (if I'm playing high gain) my pinky loops around the pup to completely flatten the edge of my palm to the strings for muting. My fretting style can also mut the BE strings when naturally playing, though I prefer classical style.
I've been practicing lately using a partially-closed hand, not muting with the back of my palm and doing all the muting with my fingers and the side of my thumb. I'm sure I'll end up using palm muting again in a mixture, but I can a lot of speed withwith control with my palm up off the strings. It's good to know all the grips: