I understand how to play a pull off with one note, but what if you want to do it with say, three strings at once? Should you play a barre with one finger and somehow pull to barre with another finger? Any suggestions on this would be appreciated, thanks.

If i play that, i would do a slide instead of pull-offs.
Besides being a guitar player, I'm a big fan of the guitar. I love that damn instrument. Steve Vai

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All you gotta do is bar the 2 and 3 with your first 2 fingers. After you play the 3, you just quickly lift up your second finger. The mallcore or nu-metal preset on your amp will do the rest

Alternatively, just focus on pulling off on the lowest string. The other strings will probably make enough sound. However, I too would slide it.
On that lick, if you're trying to make it sound like whatever artist, then do the two barred fingers and pull-off. Like several others, my personal preference is to slide barred chords like that, especially if you've got a bunch of distortion on.
Quote by El Cumanés
If i play that, i would do a slide instead of pull-offs.

IMO It gives some rock if ya do it with pull-offs