Andromeda is moving toward us. It isn't a peculiar motion superimposed on a cosmological recession; it's just ordinary relative motion.
The FLRW geometry is not a background of expanding space on which matter moves. It's just what you get when you stitch together a bunch of Schwarzschild patches representing individual moving objects. If you zoom in, you see masses moving past each other, orbiting each other, and occasionally colliding. If you zoom out, you see a bumpy spacetime manifold with roughly the shape of a FLRW manifold. The farther you zoom out, the smaller the bumps look.
You can model the evolution of the universe at a large scale as a FLRW manifold, or you can model it at a smaller scale as individual gravitating lumps, but if you do both and add the results, you'll get nonsense (or, at best, twice the correct answer). There are surprisingly many published papers that do that, and the paper by Iorio that is mentioned in James K's answer is one of them. Iorio considers "a localized gravitationally bound binary system immersed in an expanding Friedmann-Lemaître-Robertson-Walker", or to put it another way, a system of clumped matter immersed in the same matter, but unclumped. The unclumped matter isn't there, so none of the effects considered in the paper exist.
See this longer answer that discusses another paper that makes the same mistake.
(If you're wondering how ordinary relative motion can lead to superluminal expansion at large scales, see this answer to the question "Can space expand with unlimited speed?". The short version is that superluminal recession speeds are possible even in special relativity if you use the cosmological definition of recession speed.)