This letter proposes a novel coded modulation scheme for two-user Gaussian multiple access channels with higher-order modulation based on the concept of delayed bit-interleaved coded modulation. The proposed scheme effectively extracts user information from superimposed signals using previously decoded results. We demonstrate that the sum capacities of the proposed scheme can achieve the theoretical limits, while the decoding thresholds, when using spatially coupled low-density parity-check codes, closely approach these limits, even when both users employ the same constellation, bit labeling, code rate, and average power. Furthermore, we show that the proposed scheme outperforms conventional methods despite reduced complexity.