  The periodicity inherent to any interferometric signal entails a fundamental
trade-off between sensitivity and dynamic range of interferometry-based
sensors. Here we develop a methodology for significantly extending the dynamic
range of such sensors without compromising their sensitivity, scale-factor, and
bandwidth. The scheme is based on operating two simultaneous,
nearly-overlapping interferometers, with full-quadrature phase detection and
with different but close scale factors. The two interferometers provide a joint
period much larger than 2{\pi} in a moir\'e-like effect, while benefiting from
close-to-maximal sensitivity and from suppression of common-mode noise. The
methodology is highly suited to atom interferometers, which offer record
sensitivities in measuring gravito-inertial forces but suffer from limited
dynamic range. We experimentally demonstrate an atom interferometer with a
dynamic-range enhancement of over an order of magnitude in a single shot and
over three orders of magnitude within a few shots, for both static and dynamic
signals. This approach can dramatically improve the operation of
interferometric sensors in challenging, uncertain, or rapidly varying,
conditions.
