Since 2008 considerable achievements in the domain of condensed matter physics are reached: an important number of usual and high-Tc superconductors (Fe-pnictides and Fe-chalcogenides) is obtained. These new compounds are many – band systems: several energy bands (both electron and hole-type) may overlap on Fermi surface. This fact leads to the necessity to take into account the interaction of different groups of charge carriers. As a result, the elaborated earlier the theory of many – band superconductors could be used [1, 2]. These researches have been conducted by scientists from many countries long before the discovery of high-Tc superconductivity and, finally turned into a new direction in the theory of superconductivity. The conclusion that HTSC can be obtained both at attractive and repulsive interaction between charge carriers seems to be very important and interesting. This fact speaks about the possibility of existence in such systems of phonon and non – phonon mechanisms of superconductivity.  The above mentioned superconductors are obtained by introducing isovalent atoms or atoms with valence different from the one of basic substance. In this case the system (FeAs plane) is doped with electrons or holes. Considering this, our works [3 - 6] on thermodynamic and magnetic properties of two – and three – band systems remain actual. For instance, the behavior of thermodynamic quantities in superconducting phase as a function of charge carrier density can be explained.  The influence of overlapping of energy bands on the Fermi surface on superconducting properties quasi-two-dimensional system and the role of taking into account the interband electron interactions are analyzed in this work. It is shown that in two – band (or many – band) system high values of Tc may appear both at attractive (Vnm>0) and repulsive (Vnm<0) interaction of electrons, namely the HTSC mechanism can be both phonon and non-phonon. In the last case, it is necessary that the values of interband interactions prevail over intraband ones (the condition V11V22 – V12V21<0 takes place when the system is doped with isovalent impurity).  Thus, it can be considered that the interaction between electrons could be the basic mechanism contributing to the appearance of high critical temperatures in the examined system. The question how to explain the prevalence of interband electron interactions (Vnm, n≠m) over intraband ones (Vnn) remains open. In our opinion, such a situation is a result of doping, which may considerably increase the interband electron interaction, or lead to the appearance of appearance of additional interband interactions due to fluctuations of order parameters of different energy bands, including interband spin fluctuations and other factors.