Interferometric tests of aspheres have traditionally relied on so-called "null correctors". These usually require significant time and expense to design and fabricate, and are specific to a particular asphere prescription. What's more, they are tedious to align and calibrate. Aspheres can also be tested without null correction (using a spherical wavefront), but such capability is extremely limited. A typical interferometer can acquire only a few micrometers of fourth-order aspheric departure due to high-density interference fringes. Furthermore, standard software packages do not compensate for the impact upon a non-null measurement of (i) the part's aspheric shape or (ii) the interferometer's optical aberrations. While fringe density and asphere compensation severely limit the practical utility of a non-null asphere measurement, subaperture stitching can directly address these issues. In 2004, QED Technologies introduced the Subaperture Stitching Interferometer (SSI(R)) to automatically stitch spherical surfaces (including hemispheres). The system also boosts accuracy with in-line calibration of systematic errors. We have recently added aspheric capability, extending non-null aspheric test capability by an order of magnitude or more. As demonstrated in the past on annular zones of nearly nulled data, subaperture stitching can extend the testable aspheric departure. We present a more generally applicable and robust method of stitching non-null aspheric phase measurements. By exploiting novel compensation schemes and in-line system error calibration, our subaperture stitching system can provide significantly better accuracy and increased testable aspheric departure over an unstitched non-null test. Examples of stitched non-null tests are analyzed in this paper, and cross-tested against corresponding null tests.