We present a phenomenological parametrization of the phase diagram of QCD as a function of temperature $T$ and baryochemical potential $\mu$. The parametrization is constructed by introducing a switching function which controls the nature of the transition between the Hadron-Resonance Gas (HRG) and Quark-Gluon Plasma (QGP) phases of nuclear matter, such that the equation of state (EOS) possesses a rapid crossover at large $T$ and small $\mu$, a critical point placed anywhere along the phase transition line, and a first-order transition at small $T$ and large $\mu$. This EOS offers a convenient phenomenological tool for assessing the possible effects of the conjectured QCD critical point on heavy-ion observables.