I Inherit Crown, my opponent Inherits Caravan Guard.
Play Band of Misfits as Crown, playing Estate twice.
.. first play of Estate, play University twice
.... first play of University, gain a Mandarin to top-deck BoM and Estate
.... second play of University, gain a Catacombs and reveal a Watchtower from hand to trash it, drawing the BoM and Estate
.. second play of Estate, play Ambassador
.... first play of Ambassador, return Estate to the supply, opponent gains Estate
.... second play of Ambassador, opponent reacts with Estate, putting it in play
.. Estate has finished resolving, call Royal Carriage
Although by all rights, I'm pretty sure we've lost track of the Estate so many times we can't actually call RC (since it doesn't know that it's the same Estate in play).