  We derive the effect of the Schr\"odinger--Newton equation, which can be
considered as a non-relativistic limit of classical gravity, for a composite
quantum system in the regime of high energies. Such meson-antimeson systems
exhibit very unique properties, e.g. distinct masses due to strong and
electroweak interactions. We find conceptually different physical scenarios due
to lacking of a clear physical guiding principle which mass is the relevant one
and due to the fact that it is not clear how the flavor wave-function relates
to the spatial wave-function. There seems to be no principal contradiction.
However, a nonlinear extension of the Schr\"odinger equation in this manner
strongly depends on the relation between the flavor wave-function and spatial
wave-function and its particular shape. In opposition to the Continuous
Spontaneous Localization collapse models we find a change in the oscillating
behavior and not in the damping of the flavor oscillation.
