  We prove a strong factorization property of interpolation Macdonald
polynomials when $q$ tends to $1$. As a consequence, we show that Macdonald
polynomials have a strong factorization property when $q$ tends to $1$, which
was posed as an open question in our previous paper with F\'eray. Furthermore,
we introduce multivariate $q,t$-Kostka numbers and we show that they are
polynomials in $q,t$ with integer coefficients by using the strong
factorization property of Macdonald polynomials. We conjecture that
multivariate $q,t$-Kostka numbers are in fact polynomials in $q,t$ with
nonnegative integer coefficients, which generalizes the celebrated Macdonald's
positivity conjecture.
