The T −x magnetic phase diagram of Mn 1 − x Fe x Si solid solutions is probed by magnetic susceptibility, magnetization and resistivity measurements. The boundary limiting phase with short-range magnetic order (analogue of the chiral liquid) is defined experimentally and described analytically within simple model ac-counting both classical and quantum magnetic fluctuations together with effects of disorder. It is shown that Mn 1 − x Fe x Si system undergoes a sequence of two quantum phase transitions. The first “underlying"quantum critical (QC) point x ∗ ∼ 0.11 corresponds to disappearance of the long-range magnetic order. This quantum phase transition is masked by short-range order phase, however, it manifests itself at finite temperatures by crossover between classical and quantum fluctuations, which is predicted and observed in the paramagnetic phase. The second QC point x c ∼ 0.24 may have topological nature and corresponds to percolation thresh- old in the magnetic subsystem of Mn 1 − x Fe x Si. Above x c the short-range ordered phase is suppressed and magnetic subsystem becomes separated into spin clusters resulting in observation of the disorder-driven QC Griffiths-type phase characterized by an anomalously divergent magnetic susceptibility χ ∼ 1/T ξ with the exponents ξ ∼ 0.5−0.6.