  Using Cayley trick, we define the notions of mixed toric residues and mixed
Hessians associated with $r$ Laurent polynomials $f_1,...,f_r$.We conjecture
that the values of mixed toric residues on the mixed Hessians are determined by
mixed volumes of the Newton polytopes of $f_1,...,f_r$. Using mixed toric
residues, we generalize our Toric Residue Mirror Conjecture to the case of
Calabi-Yau complete intersections in Gorenstein toric Fano varieties obtained
from nef-partitions of reflexive polytopes.
