When I say #"it can be up to"#, of course there is a catch. Sometimes a given set of stereoisomers are the same compound, which I will attempt to demonstrate with the one example.
Consider, #"2,3-butanediol",# #"H"_3"CCH(OH)CH(OH)CH"_3#. The carbons attached to the hydroxyl groups are potentially chiral in that, clearly, they are each attached to 4 different residues. Now the #"R, R"#, and the #"S, S"# compounds are enantiomeric; however, the #"R, S"# and the #"S, R"# isomers are IDENTICAL; i.e. they are symmetric mirror images, and one stereocentre would map onto the other upon reflection in a mirror plane. These so-called #"meso"# isomers are not optically active.
And thus in this instance, even tho there are 2 chiral centres, there are 3 geometric isomers rather than 4 because of the equivalence of the meso isomers.
