The employment of a monomer-specific “on/off switch” was used to synthesize a nine-block copolymer with a predetermined molecular weight and narrow distribution (Đ = 1.26) in only 2.5 h. The monomers consisted of a six-membered cyclic carbonate (i.e., 2-allyloxymethyl-2-ethyl-trimethylene carbonate (AOMEC)) and ε-caprolactone (εCL), which were catalyzed by 1,5,7-triazabicyclo[4.4.0]-dec-5-ene (TBD). The dependence of polymerization rate with temperature was different for the two monomers. Under similar reaction conditions, the ratio of the apparent rate constant of AOMEC and εCL [kpapp(AOMEC)/kpapp(εCL)] changes from 400 at T = −40 °C to 50 at T = 30 °C and 10 at T = 100 °C. Therefore, by decreasing the copolymerization temperature from 30 °C to −40 °C, the conversion of εCL can be switched “off”, and by increasing the temperature to 30 °C, the conversion of εCL can be switched “on” again. The addition of AOMEC at T = −40 °C results in the formation of a pure carbonate block. The cyclic addition of AOMEC to a solution of εCL along with a simultaneous temperature change leads to the formation of multiblock copolymers. This result provides a new straightforward synthetic route to degradable multiblock copolymers, yielding new interesting materials with endless structural possibilities.