To guide improved properties coincident with reduction of critical materials in permanent magnets, we investigate via density functional theory (DFT) the intrinsic magnetic properties of a promising system, R(Fe1−xCox)11TiZ with R=Y, Ce and interstitial doping (Z=H,C,N). The magnetization M, Curie temperature TC, and magnetocrystalline anisotropy energy K calculated in local density approximation to DFT agree well with measurements. Site-resolved contributions to K reveal that all three Fe sublattices promote uniaxial anisotropy in YFe11Ti, while competing anisotropy contributions exist in YCo11Ti. As observed in experiments on R(Fe1−xCox)11Ti, we find a complex nonmonotonic dependence of K on Co content and show that anisotropy variations are a collective effect of MAE contributions from all sites and cannot be solely explained by preferential site occupancy. With interstitial doping, calculated TC enhancements are in the sequence of N>C>H, with volume and chemical effects contributing to the enhancement. The uniaxial anisotropy of R(Fe1−xCox)11TiZ generally decreases with C and N; although, for R=Ce, C doping is found to greatly enhance it for a small range of 0.7