It seems not quite clear what you actually want to have and achieve.
NAS means "Network Attached Storage", so normally it is connected via LAN cables (1GbE, 10GbE or fiber), not USB or SATA.
You have a "music server" in a Streacom chassis, ok.
What is the exact model number of that chassis, FC10 Alpha?
Do you just want more space for that music server (and for that music server alone)?
Or do you want a central place to put personal documents, music, movies, series, downloads and stuff like that, that you can access from different PCs, tablets and other devices in your home?
How much space do you need?
What do you want to put on that storage (documents, music, videos, other stuff)?
Does the music server do the streaming part for music and perhaps videos (I guess it does), or is the NAS supposed to do streaming and other stuff?
So please provide more information, so that the guys here can help you.
If you just want more space for your music in your music server, then a bigger internal HDD or an external HDD for your music server would be the simplest and cheapest choice.
But if you want a central place for all your stuff, then you could and should go for a NAS.
A NAS can be put almost everywhere, you just need a power plug and a LAN connection nearby, so no need to put it into your audio shelf (but of course you can do that if you want).
To build an actual NAS into a chassis like that would be a really tight fit, because normally a NAS houses multiple HDDs (or SSDs) and has some redundancy to keep the data safe.
In that chassis, you have 2x 3.5 and 3x 2.5 HDD bays, and no options for cooling fans.
Not the best conditions for spinning HDDs, unless you go all-SSD.
