Catalytic ring-opening polymerization (ROP) of the three major types of cyclic monomers, lactides, lactones, and carbonates, showed match and mismatch between the monomer and the catalyst. Therefore, one organocatalyst that works for all of the three in ROPs by a controlled/living nature is rare in ROPs. Herein, we proposed a traceless switch organocatalysis (TSOC) strategy and demonstrated it by switching from a Brønsted acid cationic to base/conjugate-acid bifunctional mechanisms in ROPs. Ring-opening copolymerization (ROCOP) of different types of monomers of lactones to lactides, and carbonates to lactides by organocatalysis was realized through an acid plus a base, i.e. “one plus one”, approach in one pot. The TSOC was exemplified by a methanesulfonic acid (MSA)/8-diazabicyclo[5.4.0]undec-7-ene (DBU) pair, and by diphenylphosphate (DPP)/DBU pair catalysis. DPP catalyzed cationic ROPs of δ-valerolactone (VL) and trimethylene carbonate (TMC); orthogonally, “DPP plus DBU” switched it into DPP/2DBU catalyzed bifunctional ROPs of L-lactide (LA), producing sequences of PVL-b-PLA, and PVL-b-PTMC-b-PLA. Alternatively, MSA catalyzed cationic ROPs of ε-caprolactone (CL) and TMC; switching it into MSA/2DBU catalyzed ROPs afforded block copolymers of PCL-b-PLA and PCL-b-PTMC-b-PLA. All the di- and triblock copolymers were characterized using ¹H NMR, ¹³C NMR, and SEC; each showed its exact sequence length, predicted molecular weight, and narrow dispersity. An ROCOP of the three major types of carbonyl-containing cyclic monomers using a single organocatalysis platform, in one pot, via a traceless switch, and through multi-feeding of the monomers, to sequence controlled multiblock copolymers was fulfilled.