Stucco over asbestos siding - Expensive Process?
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.