There was a Star Wars/John Carter of Mars crossover in the 1980s (sort of)
In the 1980s Star Wars comic, Chris Claremont wrote a story where Princess Leia landed on the planet Shiva IV, home to “Aron Peacebringer,” a Warlord who is good at swordfighting, and his wife, a bikini wearing native princess.
The story was actually based on art from a leftover, unused issue of John Carter, Warlord of Mars, hence the amazing similarities. Walt Simonson drew Princess Leia in to Infantino’s art.
Back in the 1970s and 1980s, it was standard Marvel policy to make a “fill in” issue in advance in case a book is late, so they would have something to send out to meet deadlines. If a book was canceled early, like John Carter, Warlord of Mars was, the fill in issue ends up not being used. So, Marvel used the unpublished fill in issue’s art in the Star Wars comic, after some modifications.
This is extra-ironic because there’s a lot of talk that part of the reason that the John Carter movie was so limply marketed by Disney was that they were in talks to buy Star Wars from George Lucas, and so they had less incentive to develop franchises “in house,” leaving John Carter orphaned. (Another film I wanted to see, David Fincher’s 20,000 Leagues Under the Sea, was abandoned as a result of this change in strategy).
Bonus fact: “Aron Peacebringer’s” colossal vaguely reptilian enemy General Sk’Ar was identified as a Kaleesh in print, General Grievous’s species. Meaning that these issues introduced the Kaleesh to the Star Wars universe.