A separate electrical meter and utility line feeding it from the street, running to its own breaker box and the dedicated wiring fed from there. Full isolation from the electrical system powering the rest of the house.
Local zoning will often prohibit such an arrangement, because it could allow a multi-family home (or home with a separate business) in what might be a neighborhood limited by zoning to single-family homes. In any event - even where it would be permitted - the grounding system would almost certainly need to be common between the two systems in order to comply with NEC.
Again, the solution to the perceived problem of "noisy grounds" on an audio system is not to pursue multiple grounds, but to ensure that all the grounds are clean. And the neutrals. And the hot connections. Noise can be introduced anywhere in an electric system, not just the ground.
The link that almarg previously provided is an authoritative resource that slays many grounding myths. Here’s one of them:
" Its connection to earth is not what makes ’safety ground’ safe ... its the connection to neutral. "
That’s worth pondering as you consider that NEC requires neutral and ground to be bonded together at the service panel.