Estimation of discrete outcome specifications involves significant hypothesis testing, including multiple modelling decisions which could affect results and interpretation. Model development is generally time-bound, and decisions largely rely on experience, knowledge of the problem context and statistics. There is often a risk of adopting restricted specifications, which could preclude important insights and valuable behavioral patterns. This study proposes a framework to assist in testing hypotheses and discovering mixed-Logit specifications that best capture discrete outcome behavior. The proposed framework includes a mathematical programming formulation and a bi-level constrained optimization algorithm to simultaneously test various modelling assumptions and produce meaningful specifications within a reasonable time. The bi-level framework illustrates the integration of a population-based metaheuristic with model estimation procedures. In addition, the optimization algorithm allows the analyst to impose assumptions on the models to test specific hypotheses or to ensure compliance with literature. Numerical experiments are conducted using different datasets and behavioral processes to illustrate the efficacy of the proposed extensive hypothesis testing in terms of interpretability and goodness-of-fit. Results illustrate the ability of the proposed algorithm to reveal important insights that can potentially be overlooked due to limited and/or biased hypothesis testing. In addition, the proposed extensive hypothesis testing generates multiple acceptable solutions, thereby suggesting potential directions for further investigation. The proposed framework can serve as a decision-assistance modelling tool in various applications, involving many variables and outcomes, such as road safety analysis, consumer choice behavior, and integrated land-use and travel choice models.