In this paper, we present the experimental results on the modification of the temperature dependences of the thermopower and the Nernst coefficient in a high-temperature superconductor of the Y0.85Ca0.15Ba2Cu3Oy composition under lanthanum and praseodymium doping. We have revealed specific features of the studied impurities influence in comparison with cases of single doping which are resulted from the presence of calcium ions in the lattice. The joint quantitative analysis of the experimental temperature dependences of the transport coefficients was performed, and this allowed us to determine the values of the main energy spectrum and charge-carrier system parameters in the studied samples. We analyzed the reasons for changes in the nature of the lanthanum and praseodymium influence induced by the calcium ions’ presence in the lattice and showed that they were different. The results obtained for the modification of the energy spectrum structure under doping allowed us to explain the peculiarities of the concentration dependences of the critical temperature in the systems under study.