Multi-shape memory effect (multi-SME) in amorphous shape memory polymers (SMPs) linked with collective and cooperative rearrangements and accommodations of monomeric segments, thus leading to generation of complex thermodynamic modes. In this study, an extended domain size model is initially formulated to describe various temperature-dependent relaxation behaviors and domain transitions in amorphous SMPs. According to the Adam-Gibbs theory, a cooperative model is employed to identify the principle role of domain size in the collective dynamics of multi-SME in amorphous SMPs. The phase transition theory is then combined with multi-branch Kelvin model to describe the collective and cooperative relaxation behaviors of the SMPs with multiple transition domains. It is shown that the proposed model is able to characterize the thermomechanical transitions and multiple shape recovery processes. Finally, the model is applied to predict shape recovery behavior of SMPs with triple- and quadruple-SME, respectively, and the theoretical results are well validated by the experimental ones.