  The maximal superintegrability of the intrinsic harmonic oscillator potential
on N-dimensional spaces with constant curvature is revisited from the point of
view of sl(2)-Poisson coalgebra symmetry. It is shown how this algebraic
approach leads to a straightforward definition of a new large family of
quasi-maximally superintegrable perturbations of the intrinsic oscillator on
such spaces. Moreover, the generalization of this construction to those
N-dimensional spaces with non-constant curvature that are endowed with
sl(2)-coalgebra symmetry is presented. As the first examples of the latter
class of systems, both the oscillator potential on an N-dimensional Darboux
space as well as several families of its quasi-maximally superintegrable
anharmonic perturbations are explicitly constructed.
