How many hydrogen bonds can methanol make?
Although this was an MD study (and might be said to be somewhat dated), quoting from Matsumoto and Gubbins (Ref. 1):


  Most of the molecules are in the two-bonding state, but a
  small fraction of molecules are in the one- or three-bonding
  state, as already pointed out in previous studies. 7
  ,8


According to this study most of the methanol molecules form 2 H-bonds but ~4-7% form 3.

References


Matsumoto, M., Gubbins, KE. The Journal of Chemical Physics 93(3):1981-1994 (doi 10.1063/1.459076).