Recently harmonic interference rejection has been recognized as a crucial bottleneck of truly wide-band software defined radio transceivers. Phase and gain mismatches among mixing paths, typical for nanoscale technology nodes, severely impact the achievable rejection ratio in classical harmonic rejection transceivers. This paper proposes an alternative digital intensive architecture, which enables increased harmonic interference rejection for wide-band SDR transceivers impacted by severe gain and phase mismatches. A generic mathematical framework of the target architecture is introduced to support a systematic design space exploration for multi-path harmonic interference rejection transceivers. With the framework, an iterative on-die estimation and compensation of mismatch for both the transmitter and receiver are presented. Case study with four mixing paths shows that ideal rejection can be achieved when targeting a single dominating harmonic interferer, and joint suppression of the 3rd and 5th order harmonic interferers of at least 70 dB can be obtained under realistic radio input scenarios.