Controlled radical polymerization methods and click chemistry form a versatile toolbox for creating complex polymer architectures. However, the incompatibility between the functional groups required for click reactions and the reaction conditions of radical polymerization techniques often limits application. Here, we demonstrate how combining two complementary click reactions in a sequence circumvents compatibility issues. We employ isocyanate-amine addition on a polymer obtained by RAFT without purification, thus allowing us to work at exact equimolarity. The addition of commercially available amine-functional azido or strained alkyne compounds, yields orthogonally modified polymers, which can be coupled together in a subsequent strain promoted cycloaddition (SPAAC). The efficiency of this reaction sequence is demonstrated with different acrylate, methacrylate, and acrylamide polymers giving block copolymers in high yield. The resulting diblock copolymers remain active towards RAFT polymerization, thus allowing access to multiblock structures by simple chain extension. The orthogonality of the isocyanate-amine reaction, SPAAC and RAFT polymerization (both in terms of monomer and chain end groups) is a key advantage and offers access to functional and challenging polymer architectures without the need for stringent reaction conditions or laborious intermediate purifications.