Question 1. Can virtual particles, in particular gravitons, interfere?
Virtual particles are created and annihilated in a distance too small and a time too short to be measured. Their existence is allowed by Heisenberg's uncertainty principle, which allows a transitory violation of energy conservation in processes that endure a short enough time.
The electromagnetic interaction has a single force carrier, the photon. The weak interaction has two force carriers, the W and Z particles (with 2 signs for W). The strong interaction has 8 force carriers, the gluons.
The quantum carrier of the gravitational force is the graviton (a massless spin 2 particle). Gravitons act together in such vast numbers that there is a scant hope to seeing evidence for just one or a few.
I think that it is established that the less energetic the force carrier, the stronger is the force mediated. If gravitons can interfere, then it is likely that they would interfere destructively (chance dictates that both constructive and destructive interference are present, but destructive interference is more likely, that we can prove). From Planck's relation from quantum mechanics, that means that these gravitons will be less energetic, thus increasing the strength of the force of gravitation, over large scales.
I emphasize that the probability of graviton interference increases for large scale systems (galaxies, clusters of galaxies), and it is very small for small scales, due to the ephemeral character of the virtual particles, in this case the graviton.
Here is my second question.
Question 2. Could this lead to a solution of the dark matter problem (a more accurate analysis than sketched here, of course)? Is it possible that the accumulated tiny effects of graviton interference in the Planck region could lead to an observable deviation from the known laws of gravity at very large scales (galaxies, clusters of galaxies), thus solving the dark matter problem?