The additivity A(F) of a family F of functions from R to R is the minimum cardinality of a family G of functions from R to R with the property that f+G is a subset of F for no f:R-->R. The values of A have been calculated for many families of Darboux-like functions from R to R. We extend these results to include some families of Darboux-like functions in from Rn to R. To do this we must define a new cardinal function called generalized additivity which is much more flexible than A.