Generalized cabling conjecture for connected sums of lens spaces

Let $K$ be a knot in a 3-manifold $Y$ admitting a Seifert fibering over $S^2$ with $n\geq 3$ exceptional fibers.

Generalized cabling conjecture. If Dehn surgery on $K$ yields a connected sum of more than $n-1$ lens spaces, then there is a Seifert fibering of $Y$ where $K$ is a regular fiber.

This conjecture seeks to characterize knots in Seifert fibered 3-manifolds that admit surgeries to sufficiently large connected sums of lens spaces. It is motivated by known results for knots in $S^3$, where torus knots and their cables account for all such surgeries, and by examples of hyperbolic knots in lens spaces.