Muting 5- 6- 7- and 8-stringers (JT welcome)

[danqi]

How do you mute the B string of your 5er?
Personally I have a 4 stringer and I use the "floating thumb technique" (I think that's waht it's called). That means I rest my thumb on the string below the one that I am playing on. When I play on the G string for example I rest my thumb on the D string. When I do that I can mute the A string by also touching it with part of my thumb but I really have problems muting the E string and thus it buzzes.
I imagine this all must even be much harder with an additional low B. Probabaly also with some extra higher strings that force me to move my plucking hand even further away from the low strings so that I can't mute 'em.
My question is:
How do YOU do your muting when playing multiquadrostringers?

[Peter McFerrin]

I have no problems with floating-thumb on a fiver--but I mute with the side of my thumb, not the tip, so I can reach across multiple strings.

[Angus]

Same as Peter; thumb laid over all the strings lower than the one I'm playing. Works perfectly, though it takes a little bit of getting used to. The left hand automatically mutes the strings higher than the one I'm playing. Works perfectly though.