  The richness of dynamical behavior exhibited by the rotational states of
various solar system objects has driven significant advances in the theoretical
understanding of their evolutionary histories. An important factor that
determines whether a given object is prone to exhibiting non-trivial rotational
evolution is the extent to which such an object can maintain a permanent
aspheroidal shape, meaning that exotic behavior is far more common among the
small body populations of the solar system. Gravitationally bound binary
objects constitute a substantial fraction of asteroidal and TNO populations,
comprising systems of triaxial satellites that orbit permanently deformed
central bodies. In this work, we explore the rotational evolution of such
systems with specific emphasis on quadrupole-quadrupole interactions, and show
that for closely orbiting, highly deformed objects, both prograde and
retrograde spin-spin resonances naturally arise. Subsequently, we derive
capture probabilities for leading order commensurabilities and apply our
results to the illustrative examples of (87) Sylvia and (216) Kleopatra
asteroid systems. Cumulatively, our results suggest that spin-spin coupling may
be consequential for highly elongated, tightly orbiting binary objects.
