  Crystals form regular and robust structures that under extreme conditions can
melt and recrystallize into different arrangements in a process that is called
crystal metamorphism. While crystals exist due to the breaking of a continuous
translation symmetry in space, it has recently been proposed that discrete
crystalline order can also emerge in time and give raise to a novel phase of
matter named discrete time crystal (DTC). In this paper, we join these two
ideas and propose a model for quantum metamorphism between two DTCs of
different periodicity, a 2T and 4T-DTC. In our model the conditions for
metamorphism come from the modulation of perturbative terms in the 4T-DTC
Hamiltonian that gradually melt its structure and transform it into a 2T-DTC.
This process is studied in detail from the viewpoint of manybody physics of
periodically driven systems. We also propose a protocol to experimentally
observe quantum metamorphism using current quantum technology.
