We demonstrate a novel multi-stage amplification scheme for self-amplified spontaneous-emission Free Electron Lasers for the production of few femtosecond pulses with very high power in the soft X-ray regime. The scheme uses the fresh-slice technique to produce an X-ray pulse on the bunch tail, subsequently amplified in downstream undulator sections by fresh electrons. With three stages amplification, X-ray pulses with an energy of hundreds of microjoules are produced in few femtoseconds. For single-spike spectra X-ray pulses the pulse power is increased more than an order of magnitude compared to other techniques in the same wavelength range. Show Partial Abstract