  Simultaneous measurements of neutron star masses and radii can be used to
constrain deviations from general relativity (GR) as was recently demonstrated
for the spontaneous scalarization model of Damour and Esposito-Far\`{e}se
(DEF). Here, we investigate the general applicability of the same procedure
beyond this single example. We first show that a simple variation of the DEF
model renders the same mass-radius measurements ineffective for obtaining
constraints. On the other hand, a recently popular and distinct model of
scalarization that arises in scalar-Gauss-Bonnet theory can be constrained
similarly to the original DEF model, albeit due to a slightly different
underlying mechanism. These establish that using the mass-radius data can
potentially constrain various theories of gravity, but the method also has
limitations.
