The magnetic field–temperature (B–T) phase diagram of the Mn0.9Co0.1P single crystal is studied in the vicinity of the Lifshitz point by means of isothermal magnetocaloric coefficient (MT) and alternating current (AC) susceptibility measurements. Results confirm previously reported shape of the B–T phase diagram and locations of characteristic temperatures and fields. At the Curie temperature (TC) the critical exponent ω, which describes a singularity of MT as a function of magnetic field (), is estimated for B parallel to the easy axis to be equal to ω ≈ 0.35. Below TC an evidence of a new enigmatic phase, reported previously for pure manganese phosphide (MnP), is found in susceptibility data also for Mn0.9Co0.1P. However, the range of existence of this phase is significantly larger here, than in MnP. At the LP we observe a sharp peak in the imaginary part of the magnetic susceptibility. A phenomenological theory is introduced to describe the field dependence of the critical lines from the disordered phase (paramagnetic) to ordered phases (ferromagnetic and modulated). The temperature and field dependences of the magnetocaloric coefficient and susceptibility are also calculated within the same framework.