Chimeric antigen receptor (CAR) T cells are a promising new approach in cancer immunotherapy. Their safety, efficacy and phenotype depend heavily on the design of the CAR, which intracellular tail contains up to three domains derived from a range of cellular signalling receptors. Due to its modular design and the multitude of possible domains, there is a vast combinatorial space of CAR designs. There are substantial efforts to improve CAR T cells based on CAR designs. However, testing the effect of each CAR design experimentally is very resource and labour intensive, and not feasible beyond a few hundred different combinations. Therefore, we aim to predict T cell phenotypes upon expression of different CAR designs, informed by single-cell RNA sequencing of a small library of 30 CAR designs using combinations of five different domains. Exploiting a prior knowledge signalling network, we design models of signalling pathways. We evaluate multiple network algorithms linking CAR domains to the phenotype of T cells, including flow maximisation, integer linear programming and pathway signal flow. As a result, we will present an interpretable model that identifies pathways activated by different CAR designs, predict the phenotype of CAR T cells and guide CAR T cell therapy.