Using high-throughput automation of ab-initio impurity-embedding simulations we created a database of 3d and 4d transition metal defects embedded into the prototypical topological insulator (TI) Bi₂Te₃. We simulate both single impurities as well as impurity dimers at different impurity-impurity distances inside the topological insulator matrix. We extract changes to magnetic moments, analyze the polarizability of non-magnetic impurity atoms via nearby magnetic impurity atoms and calculate the exchange coupling constants for a Heisenberg Hamiltonian. We uncover chemical trends in the exchange coupling constants and discuss the impurities' potential with respect to magnetic order in the fields of quantum anomalous Hall insulators. In particular, we predict that co-doping of different magnetic dopants is a viable strategy to engineer the magnetic ground state in magnetic TIs.