We prove that there exist almost-Milyutin spaces whose projection
constants are numbers of the form $1+2\sum_{i=1}^{r}\left(1-\frac{1}{n_{i}}\right)$,
where $n_{1},...,n_{r}$ are integers greater than 1. This generalizes
our earlier results, where we showed the existence of almost-Milyutin
spaces with exact projection constant greater or egual to n, for each
positive integer n.
