First, off ignore anyone who claims you "you can't do that". That's not how science has ever progressed. Post #6, however, IS valuable because it explains obstacles which must be overcome.
Of course you can model anything you want mathematically. How well it matches the actual situation involved is another matter. That likely involves lots of trial and error, calculations,etc...not an easy task...
Likely there are such models around to start...surely NASA must use such for space travel, for example. The Earth's orbit around the sun for example, likely has little to do with distant galaxies as gravity varies by the inverse square of distance...And likely you could include the effects of a few if necessary by approximating them as a single source. But nearby planets in our own solar system probably do have an effect.
For a particle, I wonder if cosmic microwave background radiation has an effect? Surely particles from our own sun have an effect that must be considered.
On the other hand, I did read about some abberations in planned trajectories of vehicles headed for Mars, I think...am unsure if those were ever sorted out...it would be interesting to know if dark energy and dark matter have any effect on our local orbit...perhaps such effects tend to cancel due to the overall uniformity of the cosmos?
Lots to consider...