Link Recommendation (LR) in complex networks has attracted huge interest in the social and computer science communities. Numerous networks, such as recommendation systems and social networks (which facilitate user contact), are probabilistic rather than deterministic due to the uncertainty surrounding the presence of links. Evaluating the various characteristics of such networks has frequently been tricky as the Intra-layer linkage graph requires at least two nodes to be in the same layer. Moreover, many existing LR methods mainly operate well on Single-Layer Graphs (SLGs) compared to Multi-Layer Graphs (MLGs) when nodes traverse multi-layers in a network of Intra-layer linkages. Considering this drawback, this paper proposes a Multi-Layer Stochastic Block Interaction method driven by Logistic Regression (MLSBI-LR) to exploit the bi-directional resources associated with Intra-layer linkages. Its inherent dependence on knowledge-based systems uses multi-criteria recommender systems to accommodate additional criteria and can modify neighborhood-based approaches. A multi-criteria network with relations over the same set of nodes is used since the modified neighbor-based method can exhibit rich dependence between entities and have available experimental data sets in MLGs to recommend links that would efficiently enrich users' experience. The accuracy and robustness of the proposed MLSBI-LR method compared to existing LR methods were extensively investigated using three distinct benchmark data sets and four evaluation metrics. Based on our experimental results across the databases and metrics, the proposed MLSBI-LR method performed significantly better (recording up to 17% increment in accuracy), recommending potential links in MLGs. Consequently, the proposed method may revolutionize link recommendation tasks in social networks by improving users' overall experience.