The dielectric constant of multiferroic hexagonal HoMn O3 exhibits an unprecedented diversity of anomalies at low temperatures (1.8 K<T<10 K) and under external magnetic fields related to magnetic phase transitions in the coupled system of Ho moments, Mn spins, and ferroelectric polarization. The derived phase diagram is far more complex than previously assumed including reentrant phases, phase transitions with distinct thermal and field hysteresis, as well as several multicritical points. Magnetoelastic interactions introduce lattice anomalies at the magnetic phase transitions. The reevaluation of the T-H phase diagram of HoMn O3 is demanded.