Only one as in MHC class I molecules, Arghyadeep. However, the number of different MHC class II molecules may be increased by the combination of alpha and beta-chains encoded by different chromosomes in heterozigous individuals. Two alpha chains and two beta chains can give rise to four different proteins, each of them forms own peptide binding cleft.

Removed by me !

As Dmitry noted, there can be multiple combinations of alpha and beta within an individual. So while each molecule (MHC receptor) only has one binding site, there can be multiple binding sites on the surface of a cell. In humans there are generally, three classical MHC class I loci and three MHC class II loci, which means any given individual could express up to 6 binding clefts on their cell surface.

one a single peptide can be presented in the MHC I or II. but the specificity of the each peptide binding cleft of MHC I/II is promiscuous...MHC I diversity is determined only by the alpha chain while is MHC II both alpha and beta chain contribute to the peptide binding cleft..as Brian Dixon stated there are 3 loci in MHCI/II and both parents contribute to the genes thus a single cell can express 3 different MHC I (only alpha chain) and 6 MHC II (both alpha and beta).