As long as you're not in KDP Select and thus locked into Amazon exclusivity, you can try any other venue you like without having to unpublish on Amazon. As others have said, under those circumstances, what's the point of removing your ebooks from Amazon?
Keep in mind that approximately 50% of all book sales in the US are on Amazon, and the percentage is much higher if we're just looking at ebooks (about 80%). Even if the other platform required exclusivity, what could it possibly offer you that would make such a thing worth it?
And if, as you said, the other platform doesn't require exclusivity, how does removing yourself from Amazon improve your trial enrollment at the other place? If you're thinking your fans will follow you to Brand X Online Bookstore, well, you have better fans than mine! Bestselling indies may go wide, but I can't think of a single example of one leaving Amazon. That would suggest they haven't found a way to make more profit by excluding Amazon.
Look at it this way. If you keep Amazon as is, you have Amazons sales, and you have other platform sales. If you exclude Amazon, you have only the sales from the other platform. The sales on the other platform won't increase if you drop Amazon. Even if, by some miracle, every single sale you would have had on Amazon miraculously migrates to the other platform, the best you've done is to break even. And in order to break even, you've taken a huge risk.
There are many valid criticisms of Amazon. But being on it won't somehow magically cause sales elsewhere to drop. That's just not how it works (unless you're in Select, and often KU makes up for it in that case).
Am I missing something?
And if by some change the folks on the new mystery platform are encouraging you to leave Amazon, run away--fast. It's almost certainly a scam of some kind.