Work with Nightbot devs to so music plays while streaming but not be part of the saved recording
A lot of streamers use Nightbot for music. If Twitch could work with them so that music is overlaid over streams only while they're live, but not saved, that could fix the problem with copyrighted music causing VODs to be muted. We could also export to YouTube without having to worry about copyright either. I believe this could be easier to implement than multiple audio channels. You would probably want to scan the VODs for copyrighted music anyway, but at least this way it's likely streamers won't have music in their VODs.

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SimonMShirley commented
The problem over copyrighted music applies to live streams as well as recorded VODs. It is no more legal for music to be streamed live as it is as a recorded clip.
Streamers should only be using Nightbot for music if they have the relevant licenses to do so.