All of the electrical grounds in a home must be bonded to the same ground point. You’ll be violating all sorts of safety codes if you attempt to do otherwise and they are there for good reason.
What you can do is dedicate grounds for your outlets (even running insulated ground wires) from the panel.
If you got an isolated service (independent meter) you could then use a truly isolated ground for things fed from that meter.
There are some in-panel ground isolators, which have a major downside. They are basically large inductors, that meet the NEC requirements for adequate ground current, BUT !!! They degrade the performance of most surge protectors.