As hydrogen bond acceptor can form two hydrogen bonds (using the two lone pairs of electrons of the oxygen atom), as hydrogen bond donator can form two hydrogen bonds (using the two hydrogen atoms in the molecule) ...
Water molecule can have/form a maximum of four hydrogen bonds: two given through the H atoms (towards two other H2O molecules), and two received on the O atom (from H atoms of two other H2O molecules).
This is the normal situation in ice, in the liquid phase the average number of hydrogen bonds decreases somewhat (more so with increasing T) but remains close to four.
A single water molecule can participate in a maximum of four hydrogen bonds because it can accept twobonds using the lone pairs on oxygen and donate twohydrogen atoms.
It is not limited to four. It can have more than four. The lone pair orbital of oxygen can share with two hydrogens and can form two hydrogen bond in a lone pair orbital. That depends on their geomatical position and the distance. When the O-H-O angle is more than about 110 degree it can be considered as a hydrogen bond. In addition to this, a hydrogen atom can form two such hydrogen bonds which are called "bifurcated hydrogen bonds". Therefore, it can form more than four hydrogen bonds (maybe eight hydrogen bonds).
In by Linus Pauling, page 467, Pauling tell us the possible combination number for n water molecules is (3/2)^n. I think it should has connection with the number of the h-bond for the n particle system.