Slightly different from the request, but what Rabby does is make Current Chain not matter. So if I connect to Tokemak on Ethereum Mainnet and have Quickswap (Polygon) open in another window both should function connected to their respective networks, at the same time.

for a multichain app, like Aave, it would connect to the last network it used and could switch, after approval, without changing the connection for everything else.