What type of siding are you considering asbestos siding? and what do you mean by stucco? masonry stucco or an Exterior Insulating Finishing System (EIFS). Anytime you are installing a new siding over an existing siding material the existing siding material must be sound. I always remove the existing siding before installing the new. It just makes for a better job, e.g. doesn't bury the window trim and, when appropriate, allows for a house wrap to reduce air infiltration. It would benefit you to post a photo of the existing.
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