In a Star Trek fan fiction, I was planning to have the crew use subspace domains to travel to another galaxy, but I don't know if this is actually possible in canon. In the Star Trek universe, can subspace domains be used to travel to different galaxies?
You could also go anywhere when you go Warp 10/infinity speed!, but even then the story doesn't really venture a day or two from Voyager. Likewise, Q or the Traveler also go "everywhere", but without the need for pesky ships.
Looking up some other galaxies in Memory Beta, the repository for non-canon Star Trek works, it mentions that the Andromeda Galaxy has been lightly explored via transwarp corridor
Both the Andromeda and Milky Way galaxies are connected by a transwarp corridor which increases the travel speed of transwarp voyages between the void, the USS Monitor during transwarp trials accidentally found its way into this corridor and was stranded between galaxies as a result.
Other "galaxy ships" (not Galaxy-class) were built for intergalactic exploration
In the 2280s, Starfleet had begun to look at exploring the Andromeda Galaxy and sent several long-range starships, including the USS Magellanic Clouds, to investigate.
You could trace through more pages on Memory Beta to find something to build off of that would work for you. If you want a looser list of dimensional Trek techno-babble, see parallel universe.
Voyager, by its premise, has come across lots of ways to maybe get home quicker, and they basically all fail. Let's say you wanted to get to the Large Magellanic Cloud (160 kly) or the Andromeda Galaxy (2.5 Mly). Their normal sustained warp would do the 75 kly in 75 years, so at a normal pace it'd take 160/2500 years.
Displacement wave from the Caretaker Array (75 kly in minutes(?)) could get you there in minutes/hours.
Wormhole flavors (instant)
- Quantum Slipstream from "Hope and Fear", mentioned doing 300 ly/h, so would take 20 days/1 year for LMC/Andromeda. Species 116 had it working on the "USS Dauntless" while Voyager's own was unstable and killed most of the crew.
- Borg Transwarp from "Dark Frontier", did 20 kly in some unspecified time in the episode epilogue. Assuming 3 days, it's basically identical to the slipstream above. Also consumable, or that's just a side effect of some incompatibility.
- Subspace vortex from Enterprise, that at 180 ly/h would take 37 days/1.5 years. Note that this is way faster than TNG/VOY tech despite being centuries older.