  The first-order electroweak phase transition in the early universe could
occur in multiple steps leading to specific multi-peaked signatures in the
primordial gravitational wave (GW) spectrum. We argue that these signatures are
generic phenomena in multi-scalar extensions of the Standard Model. In a simple
example of such an extension, we have studied the emergence of reoccurring and
nested vacuum bubble configurations and their role in the formation of multiple
peaks in the GW spectrum. The conditions for potential detectability of these
features by the forthcoming generation of interferometers have been studied.
