Ok, I was wrong about two being the record, so here's a new version.

Here's a different version:

Technically the sun counts as an astronomical body. This means any spacecraft that has visited Mars has visited 3 astronomical bodies. If you count us as right now orbiting the sun (and the galactic center) then there's even more positive examples.

@Mqrius Ah, hmm. Looks like my criteria here were poor. I think my "the record is two" comment indicates I didn't mean to count the sun, so I guess I should just exclude that body.

@IsaacKing Yeah, I agree any reasonable reading would exclude the sun, but I prefer relying on the specificity of the definition than on reasonableness where possible!

If a spacecraft starts on Earth, captures into Mars' sphere of influence, and then captures into Phobos or Deimos' SOI, does that count as 3? Same question with any of Jupiter's or Saturn's moons.

If that counts, and it sounds like it should, then we have at least one mission planned that visits Jupiter and Ganymede before 2040: JUICE

https://en.wikipedia.org/wiki/Jupiter_Icy_Moons_Explorer

With special thanks to ChatGPT

@Mqrius As long as it's in orbit around those bodies, yes.

@IsaacKing If Earth counts, hasn't Dawn already visited three bodies? It was briefly in a parking orbit around Earth, then orbited Vesta for a while, and finally orbited Ceres.

Oh, look at that.

Dawn is the first spacecraft to orbit two extraterrestrial bodies

https://en.wikipedia.org/wiki/Dawn_(spacecraft)

Any objections to me resolving this YES?

@IsaacKing no objections, sounds accurate to me! Nice find, Jacob.

It turns out that the Huygens probe also counts! It orbited Saturn and then entered Titan's atmosphere. The Cassini probe itself only did fly-bys of Titan.

When you say "there and back" - is the return trip necessary? Has a rocket travelling form the Earth to the moon visited two places, or doe sit need to return to the Earth to 'visit' it?

@Duncan Oh, right. No, the return trip isn't necessary.

What’s your definition of visit? Voyager 2 had flybys of Jupiter, Saturn, Uranus, and Neptune.

@zaphod Must decelerate to the point where it's not on an escape trajectory.