I don't know if this would work, and I don't know in relation to Apple Music. I DO know you can change and use multiple Game Center account. Also you can change you Apple ID on devices and thus possibly change Apple stores, people do this to get beta apps, or apps released in different Countries, not your own. I don't know if this would effect the music saved on the devices. It might.
You might just have to try and see. I don't believe you would ever LOSE any music, BUT you might need to download it again as you switch IDs on computers/devices. Let us know how you make out, if you try it.
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