Precompose your songs and then point the audio spectrum effect to the precomp.
Did you try it? Audio Spectrum can only be applied once to a layer and you cannot animate the audio track layer, that is obvious.
What you could do is to set up all of the audio tracks you want to use and the pre-compose the audio layers and use the pre-comp for the audio source.
If you're doing a mix then you should really be processing your audio in an audio app like Audition. AE is a lousy audio mixer, then bring in your mix and use that for the source...
This is really basic AE workflow. Make sure you go through the basics even if you have a little experience.