Not really. A tumbler service is the only one that could do that, and if they don't keep records, all you could know is all those wallets sent to the service and all those other wallets received from the service but if there are enough users of the service, you won't be able to link one to the other. It mainly depends on how many people use the service.
Though you can also do it with exchanges. Send them your dirty BTC. Switch them to another coin. Send that to your wallet (or even better, switch X% to one coin, the rest to another; create two wallets on both chains you picked, send the money there). Then do the exact same thing with another exchange. Then another. And so on.
Is it then impossible to identify you ? no, but it now requires serving warrants to many different businesses to reconstruct the chain, likely in widely different jurisdictions, and chances are some of those will be wildly uncooperative or won't keep adequate records.
Not really. A tumbler service is the only one that could do that, and if they don't keep records, all you could know is all those wallets sent to the service and all those other wallets received from the service but if there are enough users of the service, you won't be able to link one to the other. It mainly depends on how many people use the service.
Though you can also do it with exchanges. Send them your dirty BTC. Switch them to another coin. Send that to your wallet (or even better, switch X% to one coin, the rest to another; create two wallets on both chains you picked, send the money there). Then do the exact same thing with another exchange. Then another. And so on.
Is it then impossible to identify you ? no, but it now requires serving warrants to many different businesses to reconstruct the chain, likely in widely different jurisdictions, and chances are some of those will be wildly uncooperative or won't keep adequate records.