The minimal dominating set (MDS) is a well-established concept in network controllability and has been successfully applied in various domains, including sensor placement, network resilience, and epidemic containment. In this study, we adapt the local-improvement MDS routine and explore its potential for enhancing seed selection for influence maximization in multilayer networks (MLN). We employ the Linear Threshold Model (LTM), which offers an intuitive representation of influence spread or opinion dynamics by accounting for peer influence accumulation. To ensure interpretability, we utilize rank-refining seed selection methods, with the results further filtered with MDS. Our findings reveal that incorporating MDS into the seed selection process improves spread only within a specific range of situations. Notably, the improvement is observed for larger seed set budgets, lower activation thresholds, and when an "AND" strategy is used to aggregate influence across network layers. This scenario reflects situations where an individual does not require the majority of their acquaintances to hold a target opinion, but must be influenced across all social circles.