Plays a major role in regulating hemoglobin oxygen affinity by controlling the levels of its allosteric effector 2,3-bisphosphoglycerate (2,3-BPG). Also exhibits mutase (EC 5.4.2.11) activity. (2R)-3-phospho-glyceroyl phosphate = (2R)-2,3-bisphosphoglycerate + H(+) (2R)-2-phosphoglycerate = (2R)-3-phosphoglycerate At alkaline pH BPGM favors the synthase reaction; however, at lower pH the phosphatase reaction is dominant. Inhibited by citrate. Homodimer. Belongs to the phosphoglycerate mutase family. BPG-dependent PGAM subfamily.