Fair machine learning works have been focusing on the development of equitable algorithms that address discrimination of certain groups. Yet, many of these fairness-aware approaches aim to obtain a unique solution to the problem, which leads to a poor understanding of the statistical limits of bias mitigation interventions. We present the first methodology that allows to explore those limits within a multi-objective framework that seeks to optimize any measure of accuracy and fairness and provides a Pareto front with the best feasible solutions. In this work, we focus our study on decision tree classifiers since they are widely accepted in machine learning, are easy to interpret and can deal with non-numerical information naturally. We conclude experimentally that our method can optimize decision tree models by being fairer with a small cost of the classification error. We believe that our contribution will help stakeholders of sociotechnical systems to assess how far they can go being fair and accurate, thus serving in the support of enhanced decision making where machine learning is used.