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This answer to What do the shaded vertical lines in the animation of Gravity assists of space probes, mean? shows that the Pioneer 11 trajectory brought it close to both Jupiter and Saturn, and at each flyby it swung significantly up out of the ecliptic.

Why was this done... twice?

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final frame of this GIF and then plot of data from JPL's Horizons.

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    $\begingroup$ Not an answer as I don't know if this was a priority in the trajectory planning, but the flyby will give a higher velocity boost if the outgoing leg is more closely aligned with the orbital motion of the planet. It was coming down from above the ecliptic on the way in, and things may have just lined up better bouncing it back above the ecliptic than slinging it on an even steeper trajectory below it. $\endgroup$ May 17 '20 at 17:33
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According to NASA's history on the mission, Pioneer 11's goals included both investigation of the solar wind outside of the ecliptic, and a look at the polar regions of Jupiter, which appeared to have a more transparent atmosphere than the equatorial regions. A close flyby of Jupiter over either pole would unavoidably sling the spacecraft out of the ecliptic, but as we see, it was possible to incline the trajectory suitably to encounter Saturn near the spacecraft orbit's descending node with Saturn's orbit.

I'm not sure if the post-Saturn trajectory was deliberately chosen to leave the ecliptic again for further observation of the out-of-plane solar winds beyond Saturn; I think it may have been an unavoidable consequence of the choice to get a close flyby of Titan and/or to rehearse the Voyager Saturn encounters:

Pioneer 11 passed by Saturn on September 1, 1979, at a distance of 21,000 km from Saturn's cloud tops.

By this time Voyager 1 and Voyager 2 had already passed Jupiter and were also en route to Saturn, so it was decided to target Pioneer 11 to pass through the Saturn ring plane at the same position that the soon-to-come Voyager probes would use in order to test the route before the Voyagers arrived. If there were faint ring particles that could damage a probe in that area, mission planners felt it was better to learn about it via Pioneer.

Pioneer 10 was targeted at Jupiter's equatorial radiation belts, so couldn't get as far out of the ecliptic.

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