Multiresponsive poly(N-isopropylacrylamide-co-acrylic acid) (pNIPAm-AAc) microgels containing mechanically and thermodynamically decoupled poly(N-isopropylmethacrylamide) (pNIPMAm) cores have been prepared. To achieve this structure, pNIPMAm microgels were used as templates in the synthesis of an N,N'-(1,2-dihydroxyethylene)bisacrylamide (DHEA) cross-linked pNIPMAm inner shell. A pNIPAm-AAc outer shell was then added, resulting in "core/double-shell" microgels. Erosion of the inner shell via periodate-mediated cleavage of the 1,2-diol bond in DHEA produced multiresponsive core/shell microgels with independent cores. The striking structural changes and unique multiresponsivity achieved in microgels prepared via this approach illustrate the potential of multifunctional, multicomponent delivery vehicles that do not suffer from antagonistic interferences arising when different functional components are introduced within a single particle.