The way in which the "Send Page to" was designed is to share tabs with with devices related to your own account, if you want to quickly share a page to a device in your house (local network) that does not have your account but another one is not possible.
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This would be an interesting idea. Would have to think about how to make it secure/private.
There should be a few options for receiving tabs. Here are some suggestions:
If you're on macOS + iOS combination, you can do it via Handoff - https://support.apple.com/en-us/HT209455
We are currently looking at how we can improve Send tab functionality this year, and account-agnostic sharing is on our radar too. We'll keep you posted!