Multiblock copolymers represent fascinating architectures that are generally prepared from heterofunctional initiators through independent polymerization processes. So far, most of those processes exploited the nature of different monomers to simultaneously associate different kind of compatible mechanisms including ATRP, NMP, RAFT, and ROP. Herein, we demonstrate the possibility to prepare multiblock polyester-based copolymers in a "one-pot, one-step" approach from independent and simultaneous ROPs of 4- and 6-membered lactones. The independent behavior of those polymerizations appears to be possible due to the ability of 4- and 6-membered lactones to polymerize selectively by "O-alkyl" and "O-acyl" cleavages, respectively. Those two types of lactone bond ruptures have been initiated from various heterofunctional moieties bearing hydroxyl and 1,8- diazabicyclo[5.4.0]undec-7-ene (DBU)-based carboxylic salt functions. While DBU-based salts allow beta-lactones to be polymerized by an anionic process, they also act as catalyst by activating the hydroxyl dandling functions, thus polymerizing 6-membered lactones, such as L-lactide, by a H-bonding mechanism. In that work, dimethylated benzyl beta-malolactonate was used as beta-lactone representative. Depending on the initiator used, structures such as diblock, Y-shaped, and 4-arm stars have been prepared in a controlled manner in solution and at room temperature.