It can stay on as long as there are no spikes which will rock the tiles Mike. We are assuming its on the floor so you should use a powdered adhesive and make sure the minimum thickness over the old adhesive is 6mm. Obviously you will use more adhesive and to be honest its a much better job if you get the old stuff off ( ask you local tool hire company about the hire of an electric chisel for a day) but it can be done and as long as there is 6mm over the highest part of the floor its OK to do it.
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