  We study linearized perturbations of Myers-Perry black holes in d=7, with two
of the three angular momenta set to be equal, and show that instabilities
always appear before extremality. Analogous results are expected for all higher
odd d. We determine numerically the stationary perturbations that mark the
onset of instability for the modes that preserve the isometries of the
background. The onset is continuously connected between the previously studied
sectors of solutions with a single angular momentum and solutions with all
angular momenta equal. This shows that the near-extremality instabilities are
of the same nature as the ultraspinning instability of d>5 singly-spinning
solutions, for which the angular momentum is unbounded. Our results raise the
question of whether there are any extremal Myers-Perry black holes which are
stable in d>5.
