I had a metal fiddle mute that attached to the bridge and it really helped, but as it was for a fiddle and I play the five string it didn't dampen the fifth string. I am going to check out one of Rick's when I see him next.

Spartacus, you found this instrument and are trying to adapt to it. If you prefer a five string to a tenor you can usually just put a five string neck on it. Many of the vintage Five Strings that are so popular with Bluegrassers started their life as tenors.