Well-defined multiblock copolymers were synthesized via reversible addition-fragmentation chain transfer (RAFT) polymerization in a fully continuous multireactor cascade. The reactor is designed to accommodate a broad variety of monomers to be polymerized to various chain lengths close to full monomer conversion under identical conditions. Based on theoretical considerations, reactor volumes and reactant concentrations were optimized, and reactions were carried out with residence times of 40 min and at 100 °C in most cases. A broad variety of homo-, diblock-, triblock and tetrablock copolymers was obtained. The reactor can be used for high-throughput experimentation and can in principle be operated by non-specialists due to its automated character. Further, the setup allows for upscaling of reactions. The tetrablock copolymer PnBuA-b-PMA-b-PEA-b-PtBuA was obtained in quantities of 150 g in one day reactor runtime, illustrating the high potential and applicability of continuous flow processes for polymerizations.