I have two raw sound streams that I need to add together. For the purposes of this question, we can assume they are the same bitrate and bit depth (say 16 bit sample, 44.1k
I think that, so long as the streams are uncorrelated, you shouldn't have too much to worry about, you should be able to get by with clipping. If you're really concerned about distortion at the clip points, a soft limiter would probably work OK.