The possibility of controlling the domain structure in spherical nanoparticles of uniaxial and multiaxial ferroelectrics using a shell with tunable dielectric properties is studied in the framework of Landau-Ginzburg-Devonshire theory. Finite element modeling and analytical calculations are performed for Sn2P2S6 and BaTiO3 nanoparticles covered with polymer, temperature dependent isotropic paraelectric strontium titanate, or anisotropic liquid crystal shells with a strongly temperature dependent dielectric permittivity tensor. It appeared that the “tunable” paraelectric shell with a temperature dependent high dielectric permittivity (∼300 – 3000) provides much more efficient screening of the nanoparticle polarization than the polymer shell with a much smaller (∼10) temperature-independent permittivity. The tunable dielectric anisotropy of the liquid crystal shell (∼ 1 – 100) adds a new level of functionality for the control of ferroelectric domains morphology (including a single-domain state, domain stripes and cylinders, meandering and labyrinthine domains, and polarization flux-closure domains and vortexes) in comparison with isotropic paraelectric and polymer shells. The obtained results indicate the opportunities to control the domain structure morphology of ferroelectric nanoparticles covered with tunable shells, which can lead to the generation of new ferroelectric memory and advanced cryptographic materials.