  If $p : Y \to X$ is an unramified covering map between two compact oriented
surfaces of genus at least two, then it is proved that the embedding map,
corresponding to $p$, from the Teichm\"uller space ${\cal T}(X)$, for $X$, to
${\cal T}(Y)$ actually extends to an embedding between the Thurston
compactification of the two Teichm\"uller spaces. Using this result, an
inductive limit of Thurston compactified Teichm\"uller spaces has been
constructed, where the index for the inductive limit runs over all possible
finite unramified coverings of a fixed compact oriented surface of genus at
least two. This inductive limit contains the inductive limit of Teichm\"uller
spaces, constructed in \cite{BNS}, as a subset. The universal commensurability
modular group, which was constructed in \cite{BNS}, has a natural action on the
inductive limit of Teichm\"uller spaces. It is proved here that this action of
the universal commensurability modular group extends continuously to the
inductive limit of Thurston compactified Teichm\"uller spaces.
