  Let $T$ be a separating incompressible torus in a 3-manifold $M$. Assuming
that a genus $g$ Heegaard splitting $V \cup_S W$ can be positioned nicely with
respect to $T$ (e.g. $V \cup_S W$ is strongly irreducible), we obtain an upper
bound on the number of stabilizations required for $V \cup_S W$ to become
isotopic to a Heegaard splitting which is an amalgamation along $T$. In
particular, if $T$ is a canonical torus in the JSJ decomposition of $M$, then
the number of necessary stabilizations is at most $4g-4$. As a corollary, this
establishes an upper bound on the number of stabilizations required for $V
\cup_S W$ and any Heegaard splitting obtained by a Dehn twist of $V \cup_S W$
along $T$ to become isotopic.
