Interconversion of 3- and 2-phosphoglycerate with 2,3-bisphosphoglycerate as the primer of the reaction. Can also catalyze the reaction of EC 5.4.2.4 (synthase), but with a reduced activity. (2R)-2-phosphoglycerate = (2R)-3-phosphoglycerate (2R)-3-phospho-glyceroyl phosphate = (2R)-2,3-bisphosphoglycerate + H(+) Homodimer. Belongs to the phosphoglycerate mutase family. BPG-dependent PGAM subfamily.