  In this paper we consider multi-graded extended Rees algebras of zero
dimensional ideals which are Cohen-Macaulay (CM) with minimal multiplicity. We
show that the minimal multiplicity property can occur only for the ordinary
extended Rees algebra and the bigraded extended Rees algebra. For the bigraded
extended Rees algebra we find necessary conditions for it to be CM with minimal
multiplicity.
  We also produce bigraded Rees algebras which are Cohen-Macaulay with minimal
multiplicity.
