Those Bassbreakers do have master volume knobs, so you can turn them down. Of course you then miss distortion from the power amp side - which some seem to prefer. If you have 25 minutes, see a couple of goofy Englishmen try them out:
https://www.youtube.com/watch?v=KazSA5w1QOM
"What if Leo Fender talked to Pete Townshend instead of some country dudes who only want crystal clear cleans..."
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Or you could try some proper SS amps like Roland's Blues Cube series.