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A new method for multiple-input multiple-output (MIMO) detection with soft-output, the partial marginalization (PM) algorithm, was recently proposed. Advantages of the method are that it is straightforward to parallelize, and that it offers a fully predictable runtime. PM trades performance for computational complexity via a user-defined parameter. In the limit of high computational complexity, the algorithm becomes the MAP demodulator. The PM algorithm also works with soft-input, but until now it has been unclear how to apply it for other modulation formats than binary phase-shift keying (BPSK) per real dimension. In this correspondence, we explain how to extend PM with soft-input to general signaling constellations, while maintaining the low complexity advantage of the original algorithm.