It's quite common in the trombone world to drill holes in your mute. This is, first of all, quite a bit of exciting fun and experimentation; and it can be regarded as a kind of art form. However, all of that aside, it's a very common practice in order to get your instrument to play in tune when the mute is inserted and also to get certain notes (typically fairly low, or very low, ones) to speak properly.
I have NOT had to do this on my bass trombone H&B stonelined mute or on my aluminum Wick straight or adjustable cup mutes for the bass trombone, but I do have a Windy city "symphony" bass trombone mute that I had to do it on (and I now don't use that mute, favoring the Wick). I also had to do it on my tenor straight mute to get it to work well on my Olds Standard.
Since mutes on euphoniums (and tubas) are so infrequently used, I don't know if this practice is even known in the euph community. But it may be something to consider at some point. Part of the art is exactly where to drill the holes and how large they should be. I'm of the "no larger than 1/8 inch" school of thought. And the usual drill sites are either around the side perimeter at the end or in the end itself -- spaced according to your personal arcane principles. My H&B tenor mute, for example, has three holes in equilateral triangle apex configuration about 1.5" from each other. It made a huge difference.
Just a thought -- and not really trying to encourage you guys to start punching holes in your mutes.
Gary Merrill
Wessex EEb Bass tuba (DW 3XL or 2XL)
Mack Brass Compensating Euph (DE N106, Euph J, J9 euph)
Amati Oval Euph (DE 104, Euph J, J6 euph)
1924 Buescher 3-valve Eb tuba (with std US receiver), Kelly 25
Schiller American Heritage 7B clone bass trombone (DE LB K/K10/112/14 Lexan, Brass Ark MV50R)
1947 Olds "Standard" trombone (Olds #3)