In contemporary construction industry, parametric softwares are often employed in design processes of rationalization and post-rationalization where, given a certain project, the answer to specific problems is required to actualize the desired shape [problem-solving approach]. This paper outlines a research project intended to develop a generative approach to digital design where the employment of parametric and algorithmic tools provide the possibility to set up integral multi-parametric systems, organizational as well as geometrical and structural aspects are investigated and, in parallel, they inform each other. The paper unfolds through constant reference to natural systems and, more specifically, develops the notion of pluri-potential systems deriving principle from the interaction between biological processes and computation. The results address the shift from mono-parametric problem-solving approaches to a generative problem-caring process where the integration of multiple system logics contribute to the development of a virtual pluri-potential set up. Finally, the paper explore the generative interdependency between structural, geometrical, organizational and computational logics of a system studying the manifold potentials of branching structures in the attempt to explore the emergent synergy between biological processes, computation and architectural design