Chimeric Antigen Receptor (CAR) T cell therapies are a type of patient-specific cell immunotherapy demonstrating promising results in the treatment of aggressive blood cancer types. CAR T cells follow a 1:1 business model, translating into manufacturing lines and distribution nodes being exclusive to the production of a single therapy, hindering volumetric scale up. In this work, we address manufacturing capacity bottlenecks via a Mixed Integer Linear Programming (MILP) model. The proposed formulation focuses on the design of candidate supply chain network configurations under different demand scenarios. We investigate the effect of an intermediate storage upstream of the network to: (a) debottleneck manufacturing lines and (b) increase facility utilisation. In this setting, we assess cost-effectiveness and flexibility of the supply chain and we evaluate network performance with respect to: (a) average production cost and (b) average response treatment time. The trade-off between cost-efficiency and responsiveness is examined and discussed.