  In a previous paper by one of us, a "compact version" of Rubio de Francia's
weighted extrapolation theorem was proved, which allows one to extrapolate the
compactness of an operator from just one space to the full range of weighted
spaces, where this operator is bounded. In this paper, we obtain
generalizations of this extrapolation of compactness for operators that are
bounded from one space to a different one ("off-diagonal estimates") or only in
a limited range of the $L^p$ scale. As applications, we easily recover recent
results on the weighted compactness of commutators of fractional integrals and
pseudo-differential operators, and obtain new results about the weighted
compactness of Bochner--Riesz multipliers.
