This paper presents the review of three main existing agile approaches: Scrum, Lean Software Development and Kanban, which served as the basis for the development of a proposal for a new approach in Agile development. To achieve this, a description of each agile approach to software development and a comparison of their strengths and weaknesses are made. Then, the new proposal is established based on the integration of the three approaches, defining a set of metrics and developing a case study to evaluate the integration and obtain quantitative and qualitative data. The results obtained from the case study proved to be quite positive because it allowed us to comprehensively evaluate the new approach. These results represent a promising start to continue working in this line of research.