Maintenance is one of the major concerns of the industrial sector. Acquiring better levels of maintenance maturity is one of the objectives to be achieved. Therefore, prescriptive maintenance is one of the areas of recent research. Current works in literature are focused on specifics of maintenance strategies (from preventive to prescriptive), usually related to a fixed asset. No previous work has been identified regarding the methodology and guidelines to be followed to be able to evolve within the different strategies from a generic perspective. To address the lack of a methodology that shows a more evolutionary path between maintenance strategies, this paper presents Maintenance Maturity Model M3: a maturity model that identifies three areas of action, four levels of maturity, and the activities to be carried out in each of them to make progress in the maturity level of maintenance strategies. The implementation of prescriptive maintenance should be done in a gradual way, starting at the lowest levels. M3 approaches the problem from a broader perspective, analyzing the 18 different domains and the different levels of prior maturity to be considered for prescriptive maintenance. A study has also been carried out on the different maintenance actions and the applicability of the proposed M3 maturity model to the railway infrastructure maintenance is discussed. In addition, this paper also highlights future research lines and open issues.