I'm fairly sure that the Syndicate would do that. In fact, I think someone has mentioned that someone in the Syndicate -had- been doing that?
If the Syndicate truly wanted the Sultana out of favor instead of trying to facestomproll other city-states, they'd probably let her lose all face in a war and use the war to put themselves in complete power.
If the Syndicate truly wanted the Sultana out of favor instead of trying to facestomproll other city-states, they'd probably let her lose all face in a war and use the war to put themselves in complete power.