I will present a theoretical investigation of the Floquet spectrum in multiterminal quantum dot Josephson junctions biased with commensurate voltages, so that the corresponding Bogoliubov-De Gennes Hamiltonian is periodic in time. We show that the finite voltage bias turns the equilibrium Andreev bound-states into narrow resonances forming a pattern of coupled Floquet-Wannier-Stark ladders, which can be probed experimentally by measuring finite frequency noise fluctuations. A semi-classical treatment shows that the location of these ladders of resonances is controlled by a Berry phase which can take the values 0 or π depending on the values of control parameters such as contact transparencies and static linear combinations of superconducting phases. We demonstrate that such Berry phase shifts can be observed by measuring the tunneling density of states on the dot. Our results suggest that the Floquet spectrum for this class of periodically driven systems presents rich behaviors, whose experimental investigation is likely to begin in the near future.