PokéBase - Pokémon Q&A
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Or so I've heard...
https://pokemondb.net/pokebase/292733/can-you-get-unlimited-stakatakas-in-um Although your question is about all of the new Ultra Beasts, and the one I linked is about just Stakataka, it answers this question, so I'll go ahead and flag this to see what mods think.
There could be variance between them so I’ll leave this one up. If it were the other way around though and the question about Stakataka was new, I’d take that one down.
Is this about Poipole/Naganadel?
Hypothetically, yes, from trade.

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The only Ultra Beasts that are of limited quantity are the new ones. (the Poipole offered in Ultra Megalopolis and the two Blacephalon/Stakataka in Poni Grove) The old ones can be caught as many times as you wish, as they'll respawn whenever you visit their respective worlds again.

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