"The sky is not a painted backdrop, you can travel to each and every star you see. The constellations change with parallax as you explore the galaxy, and the night sky viewed from Earth is, of course, accurate." - Frontier
400 billion stars in 100 billion star systems await Elite: Dangerous commanders every day. Someone even checked that with standard ship fittings, it can take around 650 gameplay hours to get to the edge of the Milky Way starting from the center of the Solar System -- or about roughly 65,000 light years.
This shows the scale of the in-game world set by Frontier.
It also brings up the question: Do we really need to have other galaxies in Elite: Dangerous, since it seems that the Milky Way should keep players occupied for a significant amount of time? According to latest calculations made by the developer, the last unknown star system included in the game will be discovered in roughly 25,000 years. Of course, it will be interesting to see if in 255th century people will still have PC computers and time to play Elite: Dangerous.
But there is another way to answer if we really need other galaxies in the game. Lately, at least two alien races were discovered in Elite: Dangerous. And a couple of weeks ago, players discovered not only artifacts and ruins of old alien civilizations, but also space ship which belonged to Thargoids.
Although it was said in in-game lore that those aliens were coming from different dimension, this was never completely confirmed. Also, there is a good possibility that regardless of their origin, they could have outposts in the galaxies near to the Milky Way.
So, it seems that regardless how big the Milky Way is, we could see gateways to other galaxies at some point.
There are whole in-game factions dedicated to searching for and discovering this. With no doubt, those who love to explore would be more than happy to visit more than the last unknown star system of Milky Way.
Here are a few real-life galaxies that Elite: Dangerous could add in the future to fully build-out the game's universe.