We demonstrate a novel multistage 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.