Include site ID in relations for singles on multiple sites

[turnstylerj]

For multi-site installations with entry selectors set to enable "Show the site menu" in advanced options, the CMS author is able to link to entries on other sites from their current one, and we can get that entry in our templates like:

{% set selectedEntry = entrySelector.siteId('*').one() %}

This works for most scenarios, but presents a problem when the author is trying to link to the non-primary site version of a single that's enabled on both sites, as the query will find the primary site version first, and there's no way to tell if the author selected the version on the non-primary site.

Would it be possible to include site ID in entry relations, or some other way to detect which site the author selected from?