Tomlinson-Harashima precoding (THP) is a nonlinear processing technique employed at the transmit side to implement the concept of dirty paper coding (DPC). The application of THP is restricted by the dimensionality constraint that the number of transmit antennas has to be greater or equal to the total number of receive antennas. In this paper, we propose an iterative coordinate THP algorithm for overloaded scenarios in which the total number of receive antennas is larger than the number of transmit antennas. The proposed algorithm is implemented on two types of THP structures, the decentralized THP (dTHP) with diagonal weighted filters at the receivers of the users, and the centralized THP (cTHP) with diagonal weighted filter at the transmitter. Simulation results show that a significantly better bit error rate (BER) and sum-rate performances can be achieved by the proposed iterative coordinate THP algorithm as compared to previously reported techniques.