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

A bound on the number of twice-punctured tori in a knot exterior