I wonder? If Jupiter has the power to move the Sun, then other planets should be affected to. From this and the fact planet orbits are still said elliptical, I infer that other planets actually also orbit the Jupiter-Sun barycenter. Correct?
To the extent that the planets orbits can be considered elliptical, they orbit the barycenter of the entire solar system, including the Sun, Jupiter, and the other planets. Where that's located relative to the Sun-Jupiter barycenter changes a bit, as the Sun-Jupiter system as a whole orbits around the common barycenter.
But we can make some estimates for how big that offset is. The Sun-Jupiter barycenter is offset from the center of the sun by M_{Jupiter}/(M_{Sun} + M_{Jupiter}) * R_{Sun-Jupiter}, here M_{X} is the mass of X and R_{X-Y} is the distance from X to Y. At aphelion, Jupiter is at 8.16e11m from the sun according to https://en.wikipedia.org/wiki/Jupiter, and its mass is about 9.5e-4 that of the sun, so the offset ends up being about 7.8e8m. The radius of the sun is about 6.96e8m, for comparison (according to https://en.wikipedia.org/wiki/Sun).
OK, what about the other planets? Saturn is about 1/3 the mass of Jupiter and about 2x further from the sun. So its impact on the overall solar system barycenter is about 2/3 that of Jupiter. Neptune is about 18x lighter than Jupiter and about 6x further away, so that's another 1/3. Uranus is about 22x lighter than Jupiter and about 4x further away, so that's another 1/6-1/5. The other planets don't really matter for this calculation with the number of significant figures we're using, because they're both lighter and closer in (e.g. Earth is about 1/316 the mass of Jupiter and 5x closer to the sun, so its impact is about 1/1500 that of Jupiter).
So if Jupiter, Saturn, Uranus, and Neptune all happened to line up the barycenter of the Sun-Jupiter system would be about halfway between the center of the sun and the solar system barycenter. To the extent that they don't all line up, the separation between the Sun-Jupiter and overall barycenters will be smaller. And if Saturn and Neptune both line up on the opposite side from Jupiter, that puts the solar system barycenter pretty close to the center of the sun.