Clique is a fundamental model for cohesive subgraph discovery and has been extensively studied in single-layer graphs. However, in multilayer (ML) graphs, where vertices are connected through multiple types of relationships, existing studies remain limited and primarily focus on density-based models. In this paper, we propose two novel models, namely skyline ML-clique and optimal ML-clique. Specifically, given an ML graph G, a subgraph S is a skyline ML-clique if it is not dominated by any other clique in terms of both vertex set and supporting layers, while an optimal ML-clique is defined as the subgraph that maximizes a tunable function balancing clique size and layer support. We prove that the problem of enumerating all skyline ML-cliques is NP-hard, and develop a baseline enumeration algorithm along with several optimization techniques, including categorical pruning and adaptive skyline verification. For the optimal ML-clique, we further design a layered branch-and-bound framework with progressive computation to obtain high-quality solutions efficiently. Finally, extensive experiments on 7 real-world ML graphs demonstrate the effectiveness of the proposed algorithms.