  George Andrews and Ae Ja Yee recently established beautiful results involving
bivariate generalizations of the third order mock theta functions $\omega(q)$
and $\nu(q)$, thereby extending their earlier results with the second author.
Generalizing the Andrews-Yee identities for trivariate generalizations of these
mock theta functions remained a mystery, as pointed out by Li and Yang in their
recent work. We partially solve this problem and generalize these identities.
Several new as well as well-known results are derived. For example, one of our
two main theorems gives, as a corollary, a special case of Soon-Yi Kang's
three-variable reciprocity theorem. A relation between a new restricted
overpartition function $p^{*}(n)$ and a weighted partition function $p_*(n)$ is
obtained from one of the special cases of our second theorem.
