"Inverse" $(N+M)$-body problem

This question is a logical continuation of the question about "Inverse" $N$-body problem.

Let’s consider the following extension of that problem: Assume that there are $(N+M)$ particles in some space. You are given the trajectories of $N$ of these particles over some time interval. The problem is two find any possible set of trajectories for the rest $M$ particles (the initial conditions for these $M$ particles are unknown).

@atarasenko has pointed out that in general such problem can have infinitely many solutions. Quote: "For example, for $N=1$ and $M=2$; the first particle (with known trajectory) is always at the point $mathbf{r}_1(t)$, and two other particles (with unknown trajectories) are at the opposite points: $mathbf{r}_2(t)=-mathbf{r}_3(t)$. It is not possible to find $mathbf{r}_2(t)$ in this problem because the forces acting on the first particle always compensate each other. It will stay at the origin for any $mathbf{r}_2(t)$."

As in the previous problem, we can assume that each pair of particles is attracted according to the inverse square law.

I foresee that this problem doesn’t have an analytical solution in general. So any discussions on numerical ways of solving the stated problem are also welcomed.