  This paper continues a program due to Motegi regarding universal bounds for
the number of non-isotopic essential $n$-punctured tori in the complement of a
hyperbolic knot in $S^3$. For $n=1$, Valdez-S\'anchez showed that there are at
most five non-isotopic Seifert tori in the exterior of a hyperbolic knot. In
this paper, we address the case $n=2$. We show that there are at most six
non-isotopic, nested, essential 2-holed tori in the complement of every
hyperbolic knot.
