Make an ellipse.
Rotate 45*
Quad Osnap will recognize the original Quad (Ellipse Vertex) and the new Quad (outermost point). This is actually pretty cool.

Do the same with a circle and the original Quad isn’t recognized (no Vertex). Am I missing some way to enable this?

Hi Declan- I think this does not really apply to circles- it is not so much finding the original quad as finding sort of shape based quads as well as CPlane based ones- a circle does not have those.