The problem of unravelling the information contained in First Order Reversal Curves (FORC) has become in the recent years a discussion matter because the commonly used technique of assimilating the FORC diagrams to the Preisach plane is not satisfactory in many cases. This is particularly so when the magnetic interactions within the system are strong, comparable or larger than the switching fields, as in soft ferromagnets. In this work, the authors present an interpretation of this technique as a differential tool for the study of magnetic interactions without referring to Preisach models. It allows discriminating the magnetic phases of the system as well as the dominant interactions. The proposed FORC differential dissection is applied to partially crystallized ribbons of the Co69B12Si12Fe4Mo2Ni1 alloy, identifying two magnetic phases with close but different magnetic hardness which are positively coupled both internally and mutually.