https://en.wikipedia.org/wiki/Orthogonal_(series)
https://en.wikipedia.org/wiki/Diaspora_(novel)
Diaspora starts in this universe but ends up somewhere else.
Celestial Matters by Richard Garfinkle has Ptolemaic cosmology and Aristotelian physics.
The Planiverse: Computer Contact with a Two-Dimensional World by A.K. Dewdney is sort of a modern take on the classic Flatland by Edwin Abbot, and manages to improve upon it considerably.
The Long Earth series by Terry Pratchett and Stephen Baxter posits an infinite set of parallel Earths that can be reached with a trivial but unorthodox electronic device. You have to travel to them incrementally, one sideways step
Some of his other books the physics are the same as ours but the locations are so exotic that they might as well qualify.
https://www.royalroad.com/fiction/21844/i-am-going-to-die-in...
There are no advanced concepts or deep hard scifi explorations, but the various worlds each have unique physics systems that are macro-consistent.
But yeah for the other Trek technology
and you have to aim a flashlight like a water hose. +1 for the appendix at the end that explains the conceit and lays out the equations used!
One of my favorites, written by John E. Stith.
The first book is the best - subsequent books are almost pure fantasy.