Painting with water base eggshell on oil base undercoat

If painting exterior I would be cautious and use a proven system as the demands on the paint are greater outdoors. If job is indoors however, I would say there is no problem. I have used water based paint over oil based undercoat many times. In fact oil based paint is used as a stain block on walls and ceilings before applying emulsion. Same thing with wood. The only thing I can think may happen is 'fish eye' where the water based paint dimples. Just make sure the undercoat is good and dry before using eggshell and also give the undercoat a light sanding to avoid this and to give a perfect finish.