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Cheers, and @Velocio I should have thought of looking on partpicker given that's where I'm speccing the rest of the components.
Looks like the fractal design ones are probably what to go for.
I also want it to run windows so it can replace a few other things. Built up to a reasonable spec it's around £650 (not including 3.5" drives) which is a fair bit cheaper than getting a Synology one (although I imagine not as power efficient).
Cases that take 8+ 3.5" drives, cheapest first:
https://uk.pcpartpicker.com/products/case/#J=8,20&sort=price
You can also buy extra drive cages for a lot of cases, guess that is not reflected in these listings.
I think what you are looking for is increasingly obscure and priced accordingly, though.