Using Live Copy is a terrific way of quickly making variations on a tile that is set up properly, and thanks for suggesting this, Phil!
Here's an example; you have to be careful about using the Shape Builder and the Ersaer on a Live Copy that has a shadow, and I don't see where you can specify that the Live Copy lands precisely on top of the original, but none of this is a deal-breaker. All you do after Arrange>Live Copy, is select the two of them, Ctrl+Shift+L, align centrally, and you're good to go.
Try experimenting with the attached Xara file. You need the Pro version.