dimers carboxylic acids Watch
The diagram you provided would not be stable geometrically. A typical hydrogen bond is only twice as long compared to a "covalent" OH bond. Since O is sp2 hybridised, COH will be a bond angle around 120 degrees and there simply is not enough space to properly align the Oxygen lone pair to the HO covalent bond. Notice that your Oxygen on the right with 2 hydrogen bonds has both bonds coming at almost the same angle, but there is only 1 lone pair in this location.
If R was small then it may be possible to stack H bonds with an offset but again I suspect forming many dimers is the initial goal for reducing the energy of the solution. Chemical structures tend to fall down this energy well slope quickly, its a major part of what drives protein folding in cells.