  We investigate dynamics of probe particles moving in the near-horizon limit
of extremal Myers-Perry black holes in arbitrary dimensions. Employing
ellipsoidal coordinates we show that this problem is integrable and separable,
extending the results of the odd dimensional case discussed in
arXiv:1703.00713. We find the general solution of the Hamilton-Jacobi equations
for these systems and present explicit expressions for the Liouville integrals,
discuss Killing tensors and the associated constants of motion. We analyze
special cases of the background near-horizon geometry were the system possesses
more constants of motion and is hence superintegrable. Finally, we consider
near-horizon extremal vanishing horizon case which happens for Myers-Perry
black holes in odd dimensions and show that geodesic equations on this geometry
are also separable and work out its integrals of motion.
