  I address some problems encountered in the formulation of relativistic models
encompassing the MOND phenomenology of radial acceleration. I explore scalar
and vector theories with fractional kinetic terms and $f(R)$-type gravity,
demanding that the energy density be bounded from below and that superluminal
modes be absent, but also that some consistency constraints with observational
results hold. I identify configurations whose energy is unbounded from below
and formulate some no-go statements for vector field models and modified
gravity theories. Finally, I discuss superfluid dark matter as a hybrid theory
lying between CDM and modified gravity, highlighting some difficulties present
also in this case, which appears preferable to the others.
