What's the Name of That Book??? discussion

This topic is about
Another Fine Myth
SOLVED: Adult Fiction
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SOLVED. Adult Sci-Fi and/or Fantasy series. Multiple dimensions and magic? Read around early 2000s. [s]
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The protagonists travel in the Gay Deceiver, which is equipped with the "continua" device developed by one of the main characters while he was formulating his theories on n-dimensional non-Euclidean geometry. The continua device allows travel into various fictional universes, such as the Land of Oz, as well as through time.
From Wikipedia:
"In the novel, the biblical number of the beast turns out to be not 666 but {\displaystyle (6^{6})^{6}}(6^{6})^{6} or 10,314,424,798,490,535,546,171,949,056,[1] the initial number of parallel universes accessible through the continua device. It is later theorized by the character Jacob that the number may be merely the instantly accessible universes from a given location and that there is a larger structure that implies an infinite number of universes."

Makes me think of Robert Asprin's Myth series - starting with "Another Fine Myth"
Books mentioned in this topic
InterWorld (other topics)Another Fine Myth (other topics)
The Number of the Beast (other topics)
One particular scene I remember is one of the first new dimensions they travel to is a kind of lawless street market planet. There might have been a sub plot with the main character falling for the princess of his home dimension? In any case, trouble tends to chase them wherever they go... The writing style definitely had a wry humor, which kind of makes me think of Patricia C. Wrede, but aimed toward adults.
I read these books back in the early 2000s, I think, but based on what I remember about the cover possibly published in the 60s or 70s? I read them in a paperback copy that had at least two books (or maybe two parts?) with a brown cover and the alien character on the front, holding a futuristic gun, and possibly a fairy-tale style princess as well?
Thanks in advance for any help anyone can give!