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Sure. If you want to go to the US, and the trip isn't for an E-3 purpose, but does qualify you as a visitor for business or pleasure, you can enter on the VWP or a B-1/B-2 visa.
I'm not sure what would disqualify you from traveling as an E-3 but not as a B or VWP visitor, but I imagine there might be reasons such relating to your US employment, or perhaps simply wanting to visit for pleasure.
It may also be possible to travel for pleasure on your E-3, though, which would save you 14 bucks. I don't know whether that is the case.