Multiple thickness Fe foils were ramp compressed over several nanoseconds to pressure conditions relevant to the Earth's core. Using wave-profile analysis, the sound speed and the stress-density response were determined to a peak longitudinal stress of 273 GPa. The measured stress-density states lie between shock compression and 300-K static data, and are consistent with relatively low temperatures being achieved in these experiments. Phase transitions generally display time-dependent material response and generate a growing shock. We demonstrate for the first time that a low-pressure phase transformation (α-Fe to ε-Fe) can be overdriven by an initial steady shock to avoid both the time-dependent response and the growing shock that has previously limited ramp-wave-loading experiments. In addition, the initial steady shock pre-compresses the Fe and allows different thermodynamic compression paths to be explored.