  Many natural and engineering systems are simultaneously subjected to a
driving force and a stabilizing force. The interplay between the two forces,
especially for highly nonlinear systems such as fluid flow, often results in
surprising features. Here we reveal such features in three different types of
Rayleigh-B\'enard (RB) convection, i.e. buoyancy-driven flow with the fluid
density being affected by a scalar field. In the three cases different {\it
stabilizing forces} are considered, namely (i) horizontal confinement, (ii)
rotation around a vertical axis, and (iii) a second stabilizing scalar field.
Despite the very different nature of the stabilizing forces and the
corresponding equations of motion, at moderate strength we counterintuitively
but consistently observe an {\it enhancement} in the flux, even though the flow
motion is weaker than the original RB flow. The flux enhancement occurs in an
intermediate regime in which the stabilizing force is strong enough to alter
the flow structures in the bulk to a more organised morphology, yet not too
strong to severely suppress the flow motions. Near the optimal transport
enhancements all three systems exhibit a transition from a state in which the
thermal boundary layer (BL) is nested inside the momentum BL to the one with
the thermal BL being thicker than the momentum BL.
