  The question of whether a Sasakian metric can admit an additional compatible
(K-)contact structure is addressed. In the complete case if the second
structure is also assumed Sasakian, works of Tachibana-Yu and Tanno show that
the manifold must be 3-Sasakian or an odd dimensional sphere with constant
curvature. Some extensions of this result are obtained, mainly in dimensions 3
and 5.
