We perform physical and numerical experiments to study the stick -slip response of a stack of slabs in contact through dry frictional interfaces driven in quasistatic shear. The ratio between the drive's stiffness and the slab's shear stiffness controls the presence or absence of slip synchronization. A sufficiently high stiffness ratio leads to synchronization, comprising periodic slip events in which all interfaces slip simultaneously. A lower stiffness ratio leads to asynchronous slips and, experimentally, to the stick -slip amplitude becoming broadly distributed as the number of layers in the stack increases. We interpret this broadening in light of the combined effect of complex loading paths, due to the asynchronous slips, and interface aging. Consequently, the aging rate of the interfaces can be readily extracted from the stick -slip cycles, and it is found to be of the same order of magnitude as existing experimental results on a similar material. Finally, we discuss the emergence of slow slips and an increase in aging -rate variations when more slabs are added to the stack.