Document from another Site with a different Layout?

IMO, this only happens with one and only one of the following three cases:

Link. A User adds a link. The link should open on the other Site.

No problem.

Embed. A User embeds a document from another Site.

What if we design a Neutral Embed, as Tweet or Instagram Embed, so we facilitate having to deal with different Themes/Layouts.

Republish a Document. We haven't discussed this case. It is the workflow by which a publisher republishes a document from another publisher.

What if the Republisher decides the theme/layout of the republished document?