Can I get a Mute switch for the H series headsets?

No, but we used to be able to!

Mute Switch P/N 43548-01

THIS IS WAS A PUSH TO MUTE SWITCH!

Please note that the in-line mute switch (PN 27708-01) offers a soft, click-over mute rather than a momentary mute (push-to-mute). This in-line mute switch is only compatible with H-series headsets.