When total space of canonical bundle of Kaehler-Einstein manifold admits a hyperkaehler structure?

Question

Let $M$ be a Kaehler-Einstein manifold of positive scalar curvature and real dimension $4n-2$ (e.g. $\mathbb{C}P^{2n-1}$). Then the total space of canonical bundle $K(M)$ has an explicit Ricci-flat Kaehler metric, i.e. it's Calabi-Yau (as described in 'Calibrated fibrations on complete manifolds via torus Action', E. Golstein). Are there examples when $K(M)$ is hyperkaehler (possibly with metric different from described above)?