There would be no incentive for them to do so.

Arbitrage:

The energy expenditures to alter the trajectories of the entire Milky Way and/or Andromeda galaxies would be ridiculous and the benefits seem quite small (no star's are expected to collide). Further, on a very long time scale matter being more co-located is likely useful - negative entropy is valuable! Even more points against, you'd need to find some way to push one of the above galaxies sufficiently far outside of the local group to actually prevent this from happening in the very long term - all of the galaxies in our local group are highly likely to coalesce in the next 1 trillion years.