  The identification of microscopic models describing the low-energy properties
of correlated materials has been a central goal of spectroscopic measurements.
We demonstrate how 2D non-linear spectroscopy can be used to distinguish
effective spin models whose linear responses show similar behavior. Motivated
by recent experiments on the quasi-1D Ising magnet CoNb$_2$O$_6$, we focus on
two proposed models, the ferromagnetic twisted Kitaev chain with bond dependent
interactions and the transverse field Ising model. The dynamical spin structure
factor probed in linear response displays similar broad spectra for both models
from their fermionic domain wall excitations. In sharp contrast, the 2D
non-linear spectra of the two models show clear qualitative differences: those
of the twisted Kitaev model contain off-diagonal peaks originating from the
bond dependent interactions and transitions between different fermion bands
absent in the transverse field Ising model. We discuss the different signatures
of spin fractionalization in integrable and non-integrable regimes of the
models and their connection to experiments.
