This is very complex question, with many variables: i) isovalent or aliovalent substitution type, ii) ionic radii of dopant, iii) content of doping, iv) host type of cations, etc.
In many cases when you dope with aliovalent ion you create defects, i.e. vacancies, that increase conductivity (increase of dissipation factor) and permittivity (dielectric constant).
It is important, at which temperature are you going to measure dielectric constant of your material. Permittivity reaches the highest value at the point of ferroelectric phase transition. You may shift this point by doping. If to consider barium titanate, one of the factors, why incorporation of additives causes changes in dielectric properties, is the difference in polarizability betveen barium or titanium ions and ion of additive. Doping with more polirazible ions stabilizes ferroelectric state at high temperatures, increases the Curie temperature. On the opposite, doping with less polarizable ions lowers it. But if you want to shift Curie point significantly and use high concentration of dopant, you will observe diffuse phase transition, which occurs in wide temperature range. Maximum value of permittivity in case of diffuse phase transition is always lower than for undoped material.