Abstract 5D warped extra dimension models with multiple 3-branes can naturally realize multiple hierarchical mass scales which are ubiquitous in physics beyond the Standard Model. We discuss cosmological consequences of such multi-brane models with stabilized radions. It is confirmed that for temperatures below the scale of the IR brane at the end of the extra dimension, we recover the ordinary expansion of the Universe, with the Hubble expansion rate determined by sum of the physical energy densities on all 3-branes where they are localized. In addition, we explore the cosmology for temperatures above the scales of the intermediate and IR branes where the Universe is described by a spacetime with the 3-branes replaced by an event horizon. As the temperature of the Universe cools down, phase transitions are expected to take place, and the intermediate and IR branes come out from behind the event horizon. The Goldberger-Wise mechanism for radion stabilization has a well-known problem of having a supercooled phase transition, which typically does not get completed in time. This problem is even more severe when an intermediate brane is introduced, whose scale is well above TeV, as the corresponding Hubble rate is much larger. We circumvent the problem by employing an alternative mechanism for radion stabilization with dark Yang-Mills fields, which prevents a long supercooling epoch, but still allows the strong first order phase transitions. As a result, the phase transitions in our multi-brane Universe predict a stochastic gravitational wave background with a unique multi-peak signature, which is within the sensitivity reach of future space-based gravitational wave observers. We also show that there are N − 1 radions for an N 3-brane set-up, unlike a recent claim that there exists only one radion.