  Ultra-Diffuse galaxies are gravitational systems with quite varied
properties. On one hand we have cases like DF2 and DF4, both observed by the
Dragonfly Array Telescope, claimed to be highly-deficient in dark matter. On
the other hand, we have also observed dark matter dominated UDGs, such as DF44,
estimated to be at $99\%$ dark. Such variety of behaviors might be a problem
for both the standard dark matter paradigm and for alternative theories of
gravity. Here we consider a modified gravity theory belonging to the family of
Degenerate Higher-Order Scalar Tensor theories to study the internal kinematics
of both DF4 and DF44. The peculiarity of the chosen model is the partial
breaking of its Vaishtein screening mechanism for which it might have an
influence not only on cosmological but also on astrophysical scales. We
consider two different possibilities: one in which the model only plays the
role of dark energy; and another one in which it might also mimic a sort of
effective dark matter. We get conflicting results. For DF4 we confirm that the
galaxy dynamics might be successfully described even only by a stellar
component and that, at least at the scale which are probed, the content of dark
matter is quite low. In addition to that, we show that the DHOST model is
totally consistent with data and is statistically equivalent to a standard
General Relativity dark matter scenario, and it might even replace dark matter.
On the contrary, DF44 requires dark matter both in General Relativity and in
our DHOST model. When the latter is considered only as a cosmological dark
energy fluid, it is statistically fully reliable and equivalent to General
Relativity. But when we try to use it to substitute dark matter, although we
get good fits to the data, the constraints on the theoretical parameters are in
sharp contrast with those derived from more stringent probes from the stellar
scales.
