Classical planning instances are often represented using first-order logic; however, the initial step for most classical planners is to transform the given instance into a propositional representation. For example, action schemas are converted into ground actions, aiming to generate as few ground actions as possible without eliminating any viable solutions to the problem. This step can become a bottleneck in some domains due to the exponential blowup caused by the grounding process. A recent approach to alleviate this issue involves using the lifted (first-order) representation of the instance and generating all applicable ground actions on-the-fly during the search for each expanded state. In this paper, we propose a method that addresses this problem by enumerating all maximum cliques of a graph encoding the state and the action schema’s preconditions. We compare our method with state-of-the-art across 47 domains, showcasing improved performance in 23 domains. In some cases, simply changing the maximum clique enumeration algorithm results in a significant speedup compared to the state-of-the-art.