The response of soft colloids to crowding depends sensitively on the particles' compressibility. Nanogel suspensions provide model systems that are often studied to better understand the properties of soft materials and complex fluids from the formation of colloidal crystals to the flow of viruses, blood, or platelet cells in the body. Large spherical nanogels, when embedded in a matrix of smaller nanogels, have the unique ability to spontaneously deswell to match their size to that of the nanogel composing the matrix. In contrast to hard colloids, this self-healing mechanism allows for crystal formation without giving rise to point defects or dislocations. Here, we show that anisotropic ellipsoidal nanogels adapt both their size and their shape depending on the nature of the particles composing the matrix in which they are embedded. Using small-angle neutron scattering with contrast variation, we show that ellipsoidal nanogels become spherical when embedded in a matrix of spherical nanogels. In contrast, the anisotropy of the ellipsoid is enhanced when they are embedded in a matrix of anisotropic nanogels. Our experimental data are supported by Monte Carlo simulations that reproduce the trend of decreasing aspect ratio of ellipsoidal nanogels with increasing crowding by a matrix of spherical nanogels.