We present an approach for the realization of extreme off-Hugoniot states of matter in laser-driven shock experiments. The method is based on the application of impedance-mismatch effect in sandwich targets. In order to verify this model we have realized numerical simulations using the two-dimensional hydrocode multi in three-layer targets (gold-aluminum-gold) with laser intensities ∼ 10(14) W/cm(2) and obtained pressures ∼ 10 Mbar. Results show the possibility of obtaining high pressures with relatively small temperatures for a low-impedance material sandwiched between layers with high density material.