I made a guide here for installing Volumio under Proxmox which in theory would work for that.
Each instance will need to have an entire USB controller or PCI-E slot (with either a USB card or PCI-E DAC) passed through to it. Any standard motherboard from the last 10 years with either a M.2 or PCI-E 1x slot for a Wi-Fi card should be capable of running at least 4 instances, 5 if you’re OK with using the on-board audio controller.
If you have an old PC lying around then running multiple instances of Volumio on it like this would be a good option, but if you don’t then you may be better off with a fleet of RasPis