Nonpolar fluorophilic/lipophilic tetrablock amphiphiles are investigated on the surface of water and on solid substrates using compression isotherms, Brewster angle microscopy, and atomic force microscopy. At low pressures, the tetrablocks form monolayers of closely packed surface hemimicelles. Further compression causes a 2D/3D transition. At the end of the plateau, half of the deposited material is expelled forming a second monolayer on top of the initially formed monolayer. Both layers of the films consist of surface micelles, thus providing the first example of spontaneous or compression-driven stacking of self-assembled nano-objects.