An external client (that is a program that is allowed to connect to it, via for example TCP,  should be able to request an new address and to simultaneously have it internally marked within the wallet daemon process in a way so that future requests for new addresses never include this address.  At the same time, requests to watch the address should be still available.

Another way of expressing this idea is that the new address would be a secret known only by the wallet daemon, and the particular client program that asked for it and whoever or whatever the client program shares it with presumably whoever is being asked to pay.

Perhaps some of you know of several wallets that already do this.

I think these changes require a kind of wallet that needs to be backed up more than once, I doubt a change like this would be paletable to the developer of Electrum.  So please tell me which wallet daemon's have this feature if one exists.