I'm interested in writing an Alternate Mane 6 Fanfic but don't know how to start. Surely it's not as simple as throwing six random ponies together and calling it a day right.

Here's a good first step, think of who should be who and how being that pony would change who they are. Fro example who would Twilight be if she was an Earth Pony Farmer vs Applejack as an example. Think about who the characters are at their core.

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Yeah. HeartfireFirebrand has some pretty good advice.

Indeed, Twilight as an Earth pony farmer would probably be more scientific (i.e. more chemically and mechanically inclined) than Applejack to follow up on THAT example. Meaning the farm would be a bit more high-tech and have a much wider range of fruits and vegetables.

For another example, Rainbow Dash as an especially powerful unicorn instead of Twilight (Hopeful Ink Hoof has given a good example of THAT with the "Rainbow Unicorn" series) - nowhere near as bookish as Twilight, but more "learn by doing". Though, the "Sonic Rainboom" could be kept in as a REALLY powerful blast of unicorn magic that Rainbow occasionally uses as a Dangerous Forbidden Technique if she's fighting a bad guy that is powerful enough AND evil enough to push her into that Godzilla Threshold.

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Anyway, a good second step might be figuring out how certain situations would change with the alterations to the characters outside of the characters themselves.

After all, different characters, when written correctly, would have an entirely different set of experiences to somebody else and different reactions to said experiences.

My advice; find a hook, some kind of (if you'll pardon the pun) element that you can build off of.

Just as a few examples:
The Lunaverse uses the idea of Luna being the main princess to establish a different culture than the canon series, and the storytelling is more mature in tone.
The Cadanceverse has a stronger emphasis on music, both in its plot and presentation.
And because I can't resist a shameless plug, my own series features some of the more prominent background characters and adds in some elements from Doctor Who.

Basically, find a way to twist the canon series, however subtly or explicitly, and you'll be able to write something more interesting than simply, "Now these ponies are the Mane 6."

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Thanks

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Also as another note if you pick a background pony you may not have as much to work with. Also if you decided to put somepony like Celestia or Luna in that position it could become more tricky. So for example Celestia strikes me as a mix of Pinkie Pie and Fluttershy with centuries of experience.

I've done many au worlds https://www.fimfiction.net/blog/802359/the-different-view-universe being an example I think to really make a good au I think you should try to learn how the original versions behave first before changing them about. Eventually the shifted ponies might evolve over time.