We report on theoretical investigations of ferromagnetic rare-earth-transition-metal phases with the structure of YNi9In2 and with additional atoms X at two interstitial positions. By a high-throughput-screening (HTS) approach based on density functional theory the intrinsic key properties of hard magnets, namely the magnetization M, energy product (BH)max and uniaxial magnetocrystalline anisotropy constant K1 are estimated. The HTS identifies several promising phases NdFe10AX with A = Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Al, Si, P, and X = B, C, N. These phases partially outperform Nd2Fe14B in terms of (BH)max and K1 values, and they contain about 35% less rare-earth atoms.