We demonstrate the scale up of a symmetric three-path contrast interferometer to large momentum separation. The observed phase stability at separation of 112 photon recoil momenta exceeds the performance of earlier free-space interferometers. In addition to the symmetric interferometer geometry and Bose-Einstein condensate source, the robust scalability of our approach relies on the suppression of undesired diffraction phases through a careful choice of atom optics parameters. The interferometer phase evolution is quadratic with number of recoils, reaching a rate as high as 7×10^{7} rad/s. We discuss the applicability of our method towards a new measurement of the fine-structure constant and a test of QED.