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We prove that the answer to the question of the title is `as many times asyou want.' More precisely, given any constant $c>0$, we construct two obliquetriangular bipyramids, $P$ and $Q$, such that $P$ is convex, $Q$ is nonconvexand intrinsically isometric to $P$, and $\textrm{vol} Q>c\cdot \textrm{vol}P>0$.

How many times can the volume of a convex polyhedron be increased by isometric deformations?