Transversal competences constitute a set of the knowledge, skills, and attitudes required for various positions and in different professions. Such competences include: entrepreneurship, teamwork, creativity, and communicativeness; they are increasingly listed by employers in different countries as the key requirements in the labor market. The article presents the model of accelerating the process of acquiring transversal competences, developed based on the analysis of data collected in four countries of the European Union: Poland, Finland, Slovakia, and Slovenia. In the analysis, multivariate additive regression spline method was used, along with artificial neural networks, in order to create the best model describing the influence of different variables on the acceleration of acquiring transversal competences. Herewith, we demonstrated that by accelerating the acquisition of the transversal competence of entrepreneurship is influenced by the following factors: rank of the training method in the developed matrix, student numbers and the weighted average of the pace of acceleration regarding the acquisition of the remaining transversal competences, i.e., teamwork, communicativeness and creativity by the given student. The results validate our new method of the acceleration of acquiring transversal competences by students. Students may be from various higher education institutions in different countries. Developed results may be used in the course of education within the framework of the already planned vocational courses and for developing the skills required by employers for various positions and in different professions.