Airport slot scheduling has attracted the attention of researchers as a capacity management tool at congested airports. In an attempt to better grasp the demands of the problem, recent research work has employed multi-objective optimisation (MOO) approaches. However, the multiple stakeholders (e.g. airlines, coordinators, aviation and local authorities), their numerous or even conflicting objectives and the complexity of the decision-process (rules and slot priorities), have rendered the holistic modelling of the slot allocation problem a demanding and yet incomplete task. Through a rigorous review of the policy rules and the identification of the modelling gaps in the ΜΟΟ airport slot allocation literature, this study aims to contribute to the field by proposing novel modelling considerations and solution approaches which accommodate additional characteristics of the real-world decision context. In detail, by building on previous research efforts, we propose a tri-objective slot allocation model (TOSAM), which jointly considers schedule delays, maximum displacement and demand-based fairness. We further proved that multi-level, game-theoretic-based considerations are suitable to capture the interactions among the different slot priorities, leading to enhanced airport slot schedules. To address the incurring complexity, we introduced the notion of inter-level tolerance and solved the TOSAM with systematic multi-level interactions for a medium sized airport. Our computational results suggest that by tolerating small objective function sacrifices at the upper decision levels, the resulting Pareto frontiers are of greater cardinality and quality in comparison to existing solution methods. Finally, we propose and illustrate two alternative bi-stage solution methods that exemplify the potential synergies between the MOO and multi-attribute decision-making literature.