  We study the interplay between higher curvature terms and the backreaction of
quantum fluctuations in 3-dimensional massive gravity in asymptotically
(Anti-)de Sitter space. We focus on the theory at the special point of the
parameter space where the two maximally symmetric vacua coincide. In the case
of positive cosmological constant, this corresponds to the partially massless
point, at which the classical theory admits de Sitter black holes and exhibits
an extra conformal symmetry at linear level. We explicitly find the quantum
corrected black hole geometry in the semiclassical approximation and show that
it induces a relaxation of the standard asymptotic conditions. Nonetheless, the
new asymptotic behavior is still preserved by an infinite-dimensional algebra,
which, in addition to Virasoro, contains logarithmic supertranslations.
Finally, we show that all the results we obtain for the quadratic massive
gravity theory can be extended to theories including cubic and quartic terms in
the curvature.
