Superficial skin surfaces are removed mechanically or chemically with a peeling. Mechanical peeling includes microdermabrasion, medical dermabrasion and, what many people do not know, various laser treatments.
Chemical peelings include treatments with different acids that penetrate to different depths in the skin. With the depth of the treatment, however, the risks increase, so you should consider carefully whether you are willing to accept the risk of possible scarring. It’s also important to have a doctor who can explain the existing risks in detail.
As a non-professional I would never try the combination of different types of peeling and I would also leave my fingers off high-dose fruit acid peelings. Sometimes, however, a good doctor can achieve the best results for a specific skin problem by combining different peelings.