A novel approach in constructing deviations of the Kerr spacetime whereas
the symmetries can be preserved is presented. The method was applied
trivially in all known classical black-hole spacetimes tested, while
provides the possibility of testing and inventing deformations of Kerr in
a quick and innovative way. The methodology is based on earlier work by
Benenti and Francaviglia (1979) on separability of geodesic equations
while we exploited the elegant properties of Yano tensor in order to
provide an additional way of getting the Carter constant. Next, a simple,
necessary and sufficient condition in order for the aforementioned family
to have a separable Klein-Gordon equations is exhibited.
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