In this paper, we consider the design of cooperative multiple trellis coded modulation (CMTCM) schemes over Rayleigh fading channels. We design cooperative multiple trellis codes using asymmetric constellations that provide significant gains over non-cooperative coded modulation without sacrificing the data rate and bandwidth consumption. This is achieved by expanding the baseline constellation used in the non-cooperative transmission, designing the signal constellation to be asymmetric, and adopting multiple mappings by set partitioning among users. The consistent performance gains due to coding, asymmetry, and mappings of symbols onto the constellation are evaluated in terms of the frame error probability. We present simulation results that support the theoretical designs and illustrate the viability of the proposed Cooperative MTCM technique.