In fact, any system of classical physics (classical mechanics, classical field theory) is a system of fermions interacting with classical electromagnetic field and gravitational field. Why nothing more?
It is surprising that the strict mathematical formulation of relativistic mechanics (in the terms of one-dimensional submanifolds of a world manifold) describes relativistic particles interacting only with electromagnetic and gravitational fields, and nothing more, too. An equation of motion of such a particle is a geodesic equation in a pseudo-Riemannian space with a torsion, which is a strength of an electromagnetic field.
Thus, one can conclude that space-time transformations are compatible only with gravitational and electromagnetic interactions, and no others, e.g., a scalar field.
G.Giachetta, L.Mangiarotti, G.Sardanashvily, Geometric Formulation of Classical and Quantum Mechanics (WS, 2010)
G.Sardanashvily, Relativistic mechanics in a general setting, arXiv: 1005.1212