We have demonstrated the two-stage preparation of block polymers with various architectures containing mechanistically incompatible monomers. Three new monounsaturated chain transfer agents (CTAs) were synthesized containing two, four, or eight hydroxyl groups and used for the preparation of telechelic poly(cis-cyclooctene) (PCOE) by ring-opening metathesis polymerization (ROMP). We observed excellent end-group fidelity along with well-controlled molecular weights based on the initial monomer to CTA ratio. Each PCOE was subsequently used as a macroinitiator for the polymerization of d,l-lactide to produce compositionally controlled BxABx block polymers with linear (x = 1), H-shaped (x = 2), and arachne(spider)arm (x = 4) architectures. Block polymers were prepared containing PLA weight fractions (wL) ranging from 0.25-0.85. This report significantly expands on the method of combining mechanistically incompatible monomers via tandem polymerizations by introducing branched architectures that can facilitate specific property tailoring.