It is known that solid-state reaction in high-pressure oxygen can stabilize high-oxidation phases of Y-Ba-Cu-O superconductors in powder form. We extend this superoxygenation concept of synthesis to thin films which, due to their large surface-to-volume ratio, are more reactive thermodynamically. Epitaxial thin films of $rm{YBa_2Cu_3O_{7-delta}}$ grown by pulsed laser deposition are annealed at up to 700 atm O$_2$ and 900$^circ$C, in conjunction with Cu enrichment by solid-state diffusion. The films show clear formation of $rm{Y_2Ba_4Cu_7O_{15-delta}}$ and $rm{Y_2Ba_4Cu_8O_{16}}$ as well as regions of $rm{YBa_2Cu_5O_{9-delta}}$ and YBa$_2$Cu$_6$O$_{10-delta}$ phases, according to scanning transmission electron microscopy, x-ray diffraction and x-ray absorption spectroscopy. Similarly annealed $rm{YBa_2Cu_3O_{7-delta}}$ powders show no phase conversion. Our results demonstrate a novel route of synthesis towards discovering more complex phases of cuprates and other superconducting oxides.