Collaborative knowledge construction (CKC) is advanced by group members' cognitive engagement across three levels: individual-level knowledge processing and proposing, the peer-level social interactions and knowledge exchanges between two group members, and the group-level coordination and construction of knowledge across multiple group members. The interconnected and transformative relationship among three levels is an essential factor during the CKC process. Individual viewpoints can trigger peer feedback, which can be further refined by other group members; the group-level consensus can provide foundations for subsequent individual- or peer-level cognitive engagement. The group-level coordination of knowledge advancement involves the processing, synthesis, and reflection of knowledge from multiple members to reach a group consensus. However, previous analytical approaches have faced challenges in modeling distinct types of interconnections across the individual, peer, and group levels during the CKC process. To address this gap, this research employed multilayer network analysis (MNA) to model and quantify the multi-level and interconnected characteristics of CKC in a series of face-to-face, computer-supported CKC activities in China's higher education. First, small groups were categorized into the high, medium, and low levels of cognitive engagement groups. Second, multilayer networks were constructed for each category, where students' use of cognitive strategies were set as nodes, the interconnections between cognitive strategies were set as edges, and three levels (i.e., individual, peer, and group levels) were set as layers. The node-, layer-, and network-level metrics were calculated to quantify the overall characteristics of the networks, the interconnected characteristics within a level and across the three levels. The MNA results revealed that, compared to lower level of cognitive engagement groups, groups with higher cognitive engagement demonstrated (1) more influential moderate and deep cognitive strategies at group and peer levels; (2) interconnections between cognitive strategies with higher diversity, connectivity, and more balanced distribution across three levels, but relatively lower information exchanging efficiency; and (3) communities with more interconnections related to the moderate and deep cognitive strategies at peer and group levels. Based on the empirical findings, this research proposed pedagogical implications for CKC practices and analytical implications for using MNA to improve the understanding of computer-supported collaborative learning mechanisms.