Digital predistortion (DPD) is an effective way of mitigating spurious emission violations without the need of a significant backoff in the transmitter, thus providing better power efficiency and network coverage. In this paper, the IM3 subband DPD, proposed earlier by the authors, is extended to more than two component carriers (CCs) through a sequential learning solution. The DPD learning is iterated over each spurious emission generated by each pair and trio of CCs. We train and apply the DPD coefficients for the intermodulation distortion (IMD) products until a satisfactory performance is achieved. The algorithm is tested in simulations using MATLAB and in a novel, real-time implementation on a CPU via a software version of the algorithm using GNURadio.