  We consider here multitype Bienaym\'e--Galton--Watson trees, under the
conditioning that the numbers of vertices of given type satisfy some linear
relations. We prove that, under some smoothness conditions on the offspring
distribution $\mathbf{\zeta}$, there exists a critical offspring distribution
$\tilde{\mathbf{\zeta}}$ such that the trees with offspring distribution
$\mathbf{\zeta}$ and $\tilde{\mathbf{\zeta}}$ have the same law under our
conditioning. This allows us in a second time to characterize the local limit
of such trees, as their size goes to infinity. Our main tool is a notion of
exponential tilting for multitype Bienaym\'e--Galton--Watson trees.
