  Motivated by the quaternionic geometry corresponding to the homogeneous
complex manifolds endowed with (holomorphically) embedded spheres, we introduce
and initiate the study of the `quaternionic-like manifolds'. These contain, as
particular subclasses, the CR quaternionic and the $\rho$-quaternionic
manifolds. Moreover, the notion of `heaven space' finds its adequate level of
generality in this setting: (essentially) any real analytic quaternionic-like
manifold admits a (germ) unique heaven space, which is a $\rho$-quaternionic
manifold. We, also, give a natural construction of homogeneous complex
manifolds endowed with embedded spheres, thus, emphasizing the abundance of the
quaternionic-like manifolds.
