Yes its means that you ignore the effect that an object such as a spacecraft has on the central mass that it is orbiting, that the orbiting body has infinitely less mass.
Unfortunately, I think there is no exact solution found of the geodesics equations when that approximation is no longer valid or when you try to devolop geodesics equation for a spacecraft under the influence of two (or more) spherically symmetric mass distributions such as the combination of planets and the Sun in our solar system.
In the solar system JPL who calculates orbits of planets and other celestial objects use what is called the "post Newtonian expansion". You can look at their official documentation, Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation, expression 4-26 on page 4-19. Some of the the terms may be zero if you only have two non-neglibly massive objects.
Note that this is not really a "geodesics equation" per se. Nasa/JPL uses what I believe is a first order expansion of the Schwarzshild solution in isotropic coordinate and then uses a scheme I do not quite follow to get to the relativistic acceleration terms of the post-Newtonian that they add to the classical Newtonian gravitational acceleration term to calculate the orbits.
I do not know if there is a simpler way to do it.