If it's a quiet passage where you're hearing hiss, it won't necessarily be solved by getting a bigger amp. Actually, if it's a quiet passage, you're almost certainly not stressing your amp.
Since you're hearing hiss, it's coming from one of a few possible sources (in general). It may be that you're simply amplifying hiss that simple exists in the source recording. The first time I heard CD and I heard hiss, I thought there was something wrong. I thought that there should be absolutely no noise or hiss. However, it was simply there on the recording, and no storage medium will fix that. So if your source recording has a little background noise, it's very likely that it will be noticable at high volumes during quiet passages.
It's also possible that it could be that your preamp or amplifier section is a little noisy. However, with modern electronics, I find this rather unlikely. If you play no source, but turn the volume all the way up, how much noise floor do you get? (Be careful if when you have things turned up all the way) If I play no audio, but turn the volume to max, I have a slight audible hiss, but I have to have my ear right at the tweeter to hear it. If I move one or two feet from the speaker, I cannot hear the noise floor. I certainly cannot hear it from my seat.
It could also be something a little more sneaky, like a cable picking up noise or a bad connection. Do you get the noise only in on one speaker? Are your cables a rat's nest of a mess? Does the noise floor get better or worse if you move cables around or jiggle things? If so, it might be a cable or cable noise issue.
At this point, I think I'd gamble on #1 above. I think you're just amplifying the noise floor of the recording. Try different songs (especially different albums). Do they all sound the same during their quiet passages? If they're all different, and some are quiet while others are noisy, you're just hearing the recording.
Good luck!