  We explore a full dynamical phase diagram by means of a double quench
protocol that depends on a relaxation time as the only control parameter. The
protocol comprises two fixed quenches and an intermediate relaxation time that
determines the phase in which the quantum state is placed after the final
quench. We apply it to an anharmonic Lipkin-Meshkov-Glick model. This model
displays two excited-state quantum phase transitions which split the spectrum
into three different phases: two of them are symmetry-breaking phases, and one
is a disordered phase. As a consequence, our protocol induces several kind of
dynamical phase transitions. We characterize all of them in terms of the
constants of motion characterizing all three phases of the model.
