  In this paper we present an expansion of the technique of characterizing
nonlinear optics from off-energy orbits (NOECO) to cover harmonic sextupoles in
storage rings. The existing NOECO technique has been successfully used to
correct the chromatic sextupole errors on the MAX-IV machine, however, it
doesn't account for harmonic sextupoles, which are widely used on many other
machines. Through generating vertical dispersion with chromatic skew
quadrupoles, a measurable dependency of nonlinear optics on harmonic sextupoles
can be observed from hybrid horizontal and vertical dispersive orbits. Proof of
concept of our expanded technique was accomplished by simulations and beam
measurements on the National Synchrotron Light Source II (NSLS-II) storage
ring.
