Agile Project Management (APM) is supposed to replace the Traditional Project Management (TPM) in the software sector and also in many non-IT sectors. In this paper, we present the concept of project management ‘agilification’ as a smooth transition from TPM to APM. In order to develop their APM capabilities, companies need APM maturity models and scenarios to transform their project management routines. We defend that a key instrument of the TPM, which is the Project Management Maturity Model (P3M), can be adapted to APM. After identifying key principles in both TPM and APM, their convergences and divergences, this paper proposes a conceptual and practical framework consisting of behavior ontologies and two tools that facilitate this agilification: a maturity grid and a diagram displaying agilification scenarios. These proposals are applied on a case study related to the schedule management audit carried out by consultants in a large company.