The Driver Limitation for the supported number of Cards is proportional to the number of PCIe Lanes available.
With the minimum PCIe Connection being x4...
As only x16 is Dedicated to the Graphics Cards., this means that you can have a Maximum of 4 in a Desktop System.
If you were to use Threadripper this increases to 8 and Epyc this increases to 16... but that's just on a Single Board.
The Drivers do support and use ROCm (HSA) via Linux., and this will support a Network of Cards up to 512 in Total.
But again there is a Bare Minimum Bandwidth that is required for the Drivers themselves to recognise and support said Cards; and this is a DELIBERATE Design Choice. To go beyond this limit, you MUST use the Dedicated Mining Driver; which in turn MUST be running Cards with the Mining BIOS... or use a much older Driver prior to said limitation being introduced.
Said Limitation was introduced SPECIFICALLY to combat exactly what you're trying to do.
That is use Retail Hardware to build a Mining Rig.
I personally don't believe AMD went far enough with this Solution., and I think that the Drivers should be specifically rewriting the Graphics BIOS to cripple Blockchain performance on Retail and Workstation Cards.
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While the argument of "Well, it's my money I should be able to do what I want with the Cards I purchase" might seem like a reasonable one; the reality is that as it stands., the Mining Card Demands has for the past 8 years caused countless Supply Issues and grossly damaged AMD's ability to actually provide reasonable enough supply to actually increase their Market Share by any meaningful amount.
In fact even during periods where they SHOULD be seeing substantial Market Share gains; they've continued to loose ground to their Competition; almost exclusively as a result of Limited Supply in various regions.
This ultimately damages their Business, Reputation and Long-Term Profitability (remember that Mining is a Short Term endeavour; between new Crypto-Currencies emerging and garnering a "Boom" Period).
