It is not always possible to work on top of the coatings that are already in-situ if they are badly damaged, very flaky and with poor adhesion. Sometimes it is better to get everything off and start again. However, paint stripping is hard work so please do not start without taking that information on board.
The new formulations for decorative paint stripper users must, by law, not contain dichloromethane. This does not make them any harder to use than they were before. The more conventional strippers are fast acting, the more environmentally friendly strippers are slower acting but much easier and safer to handle. A personal favorite is Peelaway which uses the wrap up in a blanket and leave to soak method. Please read the product information and see which one is right for your budget, your projuct and your time frame.