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Thinking maybe a nice stabilised zoom lens would make it into a do it all machine
You have your answer ! Nikon reckon VR lenses are good for four stops, not quite as good as the IBIS in the Oly e-m1 but good enough.
Or just buy a zoom for the Olympus. The Olympus 12-50mm is dirt cheap and weather sealed. Alternatively the 12-40 f2.8 isn't too horrendously expensive for a premium lens.
Don't you already have a Nikon Df ?