[en] An observed correlation between the critical temperature of a superconducting transition in high-temperature superconductors and a proximity of their electronic structure to the topological Lifshitz transition needs to be verified on simple model materials. Here we show that such an object could be a Mo–Re alloy with an equal concentration of constituent elements. We present new evidence of the presence of two energy gaps in this material, obtained using point-contact spectroscopy, and argue that the studied Mo–Re alloy can be used for implementing new quantum effects associated with the phase difference of electron wave functions from the different bands. (author)