High order harmonic generation (HHG) from laser solid-density plasma interactions is considered as a promising way to generate bright and ultrashort burst of x-rays. One of the key issues for HHG is the low conversion efficiency due to a power law fall off in harmonic intensity. Here, we explore a possible mechanism for HHG enhancement by reflecting an intense laser pulse multiple times between two plasma surfaces. We find that HHG can be nonlinearly enhanced by orders of magnitude through multiple reflections compared with a single reflection. We argue this enhancement is due to the non-linear combination of the relativistically oscillating plasma mirror and the harmonic-rich pulse generated in preceding reflections. This mechanism should allow moderate power laser systems to efficiently generate coherent, ultrashort bursts of soft x-rays. (C) 2015 AIP Publishing LLC.