This study investigates the effect of randomness in the forcing on a harmonically excited bilinear impact oscillator with a soft barrier. The system parameter range considered coincides with regimes in which multiple stable attractors coexist. The random component superimposed on the harmonic excitations is shown to lead to qualitatively different dynamical behaviours at different parameter values, due to the presence of multiple coexisting attractors. This is classified as P-bifurcation. Wavelet analysis and recurrence quantification-based tools have been employed to show that these qualitative changes are due to noise-induced intermittency in the system. © 2020, Springer Nature B.V.