Okay, so, in order to translate this into mathematics, let's suppose we have a one-dimensional universe with two stars of the same size a distance d apart. (Or, well, a 3D universe that is redundant in every direction except on a 1D line. Gravity might work differently in an actually 1D universe. Obviously these just count the spatial dimensions; there's still time like usual.)

We can find the center easily because our toy "galaxy" is so simple. It's right in between the stars! There is no mass there (but we can imagine putting one there so we can measure gravity).

Let's measure the force, and we'll let r = d/2. The star to the left supplies a force -GmM/r^2 where m is whatever we put in between to measure the force, and the - sign means "pulling left". The star on the right supplies a force GmM/r^2, with no - sign indicating the force is to the right.

The direct force is thus -GmM/r^2 + GmM/r^2 = 0. The two cancel out, leaving no force at all. Is this what you mean by "direct expression"?

But the collective force might add instead if "the circumstances are right", GmM/r^2 + GmM/r^2 = 2GmM/r^2. Is that what you mean? It's the same gravity that was always there but it combines in different ways?

Or do you mean something completely different, like when you consider the two stars as a collective, as a galaxy, they can do some other thing with gravity that isn't really related to normal individual gravity, like, say, |f| = sqrt(GmM/r^2 * GM^2/d^2), or something else even more complicated?