While processing a modify event, I generate a move event to happen after the
current operation.
I can use Set Operation Property to add information to the modify, but not
for the new move event since it is not the current operation.
Is there a way to do this in the same policy?

The only thing I can think of is to create a new policy that checks for the
move and then add operational data to it.
But this would cause problems not having the data of the modify that I want
to put in the move event as operational data.