  We search for theories, in general spacetime dimensions, that would
incorporate a dilaton and higher powers of the scalar Ricci curvature such that
they have exact S and/or T self-dualities. The theories we find are free of
Ostrogradsky instabilities. We also show that within the framework we are
confining ourselves a theory of the form mentioned above can not have both T
and S dualities except for the case where the action is linear in the scalar
curvature.
