Needs a lot more mass than having Saturn take the plunge....needs approximately 80 times its mass before it can ignite any nuclear reactions in the core of the planet. If Jupiter had've started to form earlier on in the formation of the Sun....say as the protostellar cloud was still collapsing instead of after the Sun was pretty much complete and had an accretion disk, there may have been a chance it could've formed as a small star. Most likely an M dwarf if it snuffled up enough mass or a brown dwarf if it didn't.
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