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Most proteins in nature contain multiple folding units (or domains). The revolutionary success of AlphaFold2 in single-domain structure prediction showed potential to extend deep-learning techniques for multi-domain structure modeling. This work presents a significantly improved method, DEMO2, which integrates analogous template structural alignments with deep-learning techniques for high-accuracy domain structure assembly. Starting from individual domain models, inter-domain spatial restraints are first predicted with deep residual convolutional networks, where full-length structure models are assembled using L-BFGS simulations under the guidance of a hybrid energy function combining deep-learning restraints and analogous multi-domain template alignments searched from the PDB. The output of DEMO2 contains deep-learning inter-domain restraints, top-ranked multi-domain structure templates, and up to five full-length structure models. DEMO2 was tested on a large-scale benchmark and the blind CASP14 experiment, where DEMO2 was shown to significantly outperform its predecessor and the state-of-the-art protein structure prediction methods. By integrating with new deep-learning techniques, DEMO2 should help fill the rapidly increasing gap between the improved ability of tertiary structure determination and the high demand for the high-quality multi-domain protein structures. The DEMO2 server is available at https://zhanggroup.org/DEMO/.