It depends on the origins and roles of certain legendary Pokemon. Pokemon like Arceus, the Lake Trio and the Weather Trio are integral to the creation of the world so there should only be one of each. That doesn't however mean there can't be more of them (with exception to Arceus), as we see in HGSS's Sinjoh Ruins event that Arceus is capable of recreating Giratina, Dialga and Palkia. From that reasoning alone, any legendary excepting Arceus himself could have more than one present in the Pokemon world.
But suppose that Arceus doesn't feel like doing that or hasn't done that barring creation itself and that one-off incident. Based off of some evidence from other Pokemon media, we can see there are a few legendaries that can exist in multiples. Mew has been stated numerous times in Pokedex entries to hold DNA of all Pokemon in the world, so it follows that Mew is their common ancestor. This means there had to have been billions of them in the past. Celebi from Pokemon 4Ever is shown to have more Celebi friends who traveled to the present and brought it back from death. You could technically argue that they're past/future versions of Celebi itself, but we can't know if that's truly the case.
Pokemon Heroes shows that despite Latios sacrificing himself, there is another Lati-duo out there when watching the credits. Mewtwo has at least two present in the world, as the one in Genesect and the Legend Awakened has a different, feminine voice to that of Mewtwo in The First Movie. Likewise, we see multiple Genesect in the same film and they used to live in huge numbers in the distant past, sans the roboticization. Deoxys is known to at least have two of its kind as seen in its film as well.
Even the anime has evidence of legendaries in multiples, as we see baby Lugia Silver and its mother in the episodes The Mystery is History, A Parent Trapped! and A Promise is a Promise. Feel free to tell me of any other examples I didn't mention here.
