You wrote: "...(it) starts to break up a bit if I turn the volume way up." With a smallish speaker and a low-medium powered tube integrated amplifier, this is what is to be expected. You say the set-up has "great sound", which is most of what we are all aiming for, and I am glad for you. But this sort of rig is not meant for - and is not what one should get for - playing at REALLY LOUD volumes. It's just not going to be able to do it. The only things I would suggest you check (or have checked) to make sure everything's right is the output tube biasing (and the condition/age of those tubes if you didn't buy it new), and that the output transformer taps are 4-ohm rated. But again, since you think it sounds fine at normal volumes, my guess is that it's working as intended.
P.S. - "Clipping" just means the same thing as "breaking up"; it refers to the waveform getting squared-off at the top and bottom as amplitude surpasses the amp's ability to drive the load cleanly, producing obvious distortion products as a result.
