It is theoretically possible to write a good story with a multiverse but, practically-speaking, it’s not actually possible.

Although this is a bold statement to make: there is not a single good multiverse story.
This is due to the simple fact that multiverses are…well, they have everything. That means that you, as a writer, need to keep in mind literally every possibility that could ever happen which, get this, is impossible.
Let’s take a very basic multiverse concept into account: the idea that a new universe gets created every time a choice is made. Within the span of a few seconds of a conversation, you have just created hundreds, or possibly thousands or tens of thousands of new universes.

Why is this important? Stakes.

If a character dies…well, it literally doesn’t matter, you can just pop over to another universe and take them away. This also won’t have any negative consequences in the grand scheme of things because you hopping over and you taking them away also creates new universes. So there’s a universe where you hopped in and never took him back.
This can be extended ad infinitum so, generally, if you’re doing a multiverse story you have to be really really freaking careful with the rules. Stories like Everything, Everywhere, All at Once are bad multiverse stories.

Now, I did say above that I don’t think there’s a single good multiverse story and that’s technically true, because I don’t consider stories with ‘limited multiverses’ to be multiverse stories.
A limited multiverse is basically one in which there are some rules dictating how the multiverse works. We can technically consider Norse Mythology to have a limited multiverse, though you could also argue that Davies-era Doctor Who had a limited multiverse because traveling between multiverses was considered almost impossible and extremely dangerous. But that’s a can of worms I don’t want to get into right now.

Introducing the multiverse into a story is almost as bad as introducing time-travel, though time-travel is actually not as bad for the simple fact that you can write a good time-travel story if you’re very careful. A multiverse story is basically impossible to write well unless you’re omniscient (which you aren’t and, if you were, you’d come to the same conclusion) or you limit the rules so much that it’s no longer a multiverse.