Introduction. The implementation of the Mathematical Vertical program requires a transition from subject‑based instruction to interdisciplinary STEM project‑based learning. The proposed mechanism addresses the shortage of scientific and methodological mechanisms for integrating university and school systems for the joint design of practice‑oriented mathematical content. The aim of the study is to substantiate the experience of network interaction between a pedagogical institute and a multidisciplinary gymnasium in implementing interdisciplinary STEM projects within the framework of the “Mathematical Vertical” program, identifying the conditions for its successful implementation. Methodology and methods. The work is based on the principle of inverted distribution of roles among the participants in the educational process and is implemented through the technology of cross‑cutting interdisciplinary STEM projects to intensify students’ mastery of the program modules of the Mathematical Vertical. The study was conducted at Belgorod State National Research University and Gymnasium №2 in Belgorod. Methods of analysis, synthesis, and generalization were used, along with pedagogical observation of the dynamics of project teams, interviews with teachers, and a formative experiment. Results. The article demonstrates the pedagogical practice of jointly designing lessons by students and teachers, where students act as co‑developers, and the teacher acts as a mentor and expert. It was revealed that assigning students the role of architects of the educational environment does not reduce the quality of students’ subject‑specific training. By integrating the resources of a university and a school through the inversion of the roles of the participants in the educational process, it is possible to transform the Mathematical Vertical program from a system of advanced tutoring into a full‑fledged ecosystem for training engineering personnel, ensuring a synergistic effect for all participants in the education process.