To illustrate what I mean by 'searching for the intergalactic gas', here is an image by Thilker and Braun, which shows the low-mass gas clouds surrounding M31.
The attached image is an overlay of the gas clouds (as detected from the HI radio spectral line that originates in neutral Atomic Hydrogen Gas) over a visible-light image of M31. The gas clouds are shown as contours.
The origin and evolution of these gas clouds is unknown; some of them could be falling into M31 and may have come from intergalactic space.
Another intriguing possibility is that some of these gas clouds could be 'dark galaxies'....... containing a large concentration of dark matter, plus a small amount of gas, but with no stars formed from the gas (as yet).
These clouds, for historical reasons only, are known as High Velocity Clouds, by analogy with similar clouds that were discovered around our own Milky Way Galaxy.
(( More recently, some more distant gas clouds have been detected between M33 and M31 that may not be associated with either galaxy))