The present study focuses on the development of multiresponsive core-shell microgels and the manipulation of their swelling properties by copolymerization of different acrylamides—especially N-isopropylacrylamide (NIPAM), N-isopropylmethacrylamide (NIPMAM), and NNPAM—and acrylic acid. We use atomic force microscopy for the dry-state characterization of the microgel particles and photon correlation spectroscopy to investigate the swelling behavior at neutral (pH 7) and acidic (pH 4) conditions. A transition between an interpenetrating network structure for microgels with a pure poly-N,-n-propylacrylamide (PNNPAM) shell and a distinct core-shell morphology for microgels with a pure poly-N-isopropylmethacrylamide (PNIPMAM) shell is observable. The PNIPMAM molfraction of the shell also has an important influence on the particle rigidity because of the decreasing degree of interpenetration. Furthermore, the swelling behavior of the microgels is tunable by adjustment of the pH-value between a single-step volume phase transition and a linear swelling region at temperatures corresponding to the copolymer ratios of the shell. This flexibility makes the multiresponsive copolymer microgels interesting candidates for many applications, e.g., as membrane material with tunable permeability.