Apart from other classes of materials, supramolecular structures may exist in H-bonded liquids due to the existence of hydrogen bonding. The dynamics of these structures remains one of the most exciting topics of interest of modern science because of its crucial meaning for the behavior of water and its participation in biological processes. A special group of these liquids form monohydroxy alcohols due to their similarity to water, their ability to vitrification, and the existence of the Debye relaxation process in dielectric loss spectra reflecting the dynamics of H-bond structures. Dynamics of these structures can be studied by changes of thermodynamic conditions, by immersion of the liquid into the constraint geometry, and by dilution in a nonassociated solvent. Herein we studied the behavior of relaxation dynamics of mixtures of 2-ethyl-1-hexanol with bromobutane using broadband dielectric spectroscopy. Analysis of the results exhibits the existence of crossover in temperature dependence of static permittivity of the Debye process at some particular temperature T(c). This temperature shifts to lower values with increasing concentration of bromobutane. Moreover, below some "critical" concentration of alcohol in the mixture the shape of the Debye process loses exponentiality and the temperature dependence of relaxation times starts to change. This change was illuminated based on the analysis of the steepness index. For the lowest concentration, the value of this parameter becomes the same as the value of the steepness index of faster relaxation, called process II, of pure alcohol at ambient pressure. The observed change in relaxation dynamics with lowering concentration of alcohol is astonishingly similar to the behavior observed in the same material at elevated pressure. A possible origin of these similarities is also discussed.