  We show that the $K^*_2(1430)$, $K^*_3(1780)$, $K^*_4(2045)$, $K^*_5(2380)$
and a not yet discovered $K_6^*$ resonance are basically molecules made of an
increasing number of $\rho(770)$ and one $K^*(892)$ mesons. The idea relies on
the fact that the vector-vector interaction in s-wave with spins aligned is
very strong both for $\rho\rho$ and $K^*\rho$. We extend a recent work, where
several resonances showed up as multi-$\rho(770)$ molecules, to the strange
sector including the $K^*(892)$ into the system. The resonant structures show
up in the multi-body scattering amplitudes, which are evaluated in terms of the
unitary two-body vector-vector scattering amplitudes by using the fixed center
approximation to the Faddeev equations.
