High-resolution ultrasonic velocity measurements have been used to determine the temperature-magnetic-field phase diagram of the monoclinic multiferroic CuO. A new transition at T(N3)=230 K, corresponding to an intermediate state between the antiferromagnetic noncollinear spiral phase observed below T(N2)=229.3 K and the paramagnetic phase, is revealed. Anomalies associated with a first order transition to the commensurate collinear phase are also observed at T(N1)=213 K. For fields with B || b, a spin-flop transition is detected between 11 T-13 T at lower temperatures. Moreover, our analysis using a Landau-type free energy clearly reveals the necessity for an incommensurate collinear phase between the spiral and the paramagnetic phase. This model is also relevant to the phase diagrams of other monoclinic multiferroic systems.