Why cannot there be multiple sources for same species origins?
This is a very fundamental, and in my opinion, interesting question. You might not find many sources that directly cover this question because it is hard to test. If speciation did happen in two separate locations and the resulting species were so similar that they could breed with one another and not the original species, how would we be able to tell if the species originated in separate locations and that the new species didn't just travel to the new location? Below I'll try and explain why it's safe to assume they probably didn't have different locations for speciation.
Thought Experiment
Here is what happened in hypothetical land. Species X exists in happy land. Individuals of X then move to water land. Some more individuals from X move from happy land to H2O land (very similar to water land). Species X undergoes speciation in water land to species Y and speciation of X also occur in the H2O land to species Z.
Can Z and Y be the same species with different origins where the niche conditions are the same?
As you can imagine, the longer after geographical isolation the more mutations occur and the less likely it is that the new species will be able to breed successfully with similar species.
Although the two environments may seem identical, ecology is notoriously complex and chaotic, and so in reality as far as ecology is concerned, they are very different environments. Even the slightest difference between niches will naturally select different traits that could make Z and Y sexually incompatible.
Furthermore, when dealing with the geographical origin, you must assume that there was geographical isolation between the two speciation event locations. Since there is typically no contact between Z and Y species, there is no selective pressure to remain genetically compatible and given enough time, they will become unable to breed.

Humans
There is a contentious claim that ancient humans bred with chimpanzees after both speciation events from our common ancestor to humans and chimpanzees. Broadly I think this has now been dismissed. However, it is reasonably well accepted that in a more recent &quot;Tolkien-esque&quot; world humans bred with Neanderthals.
But ultimately I don't think there is a single example (I am thoroughly open to being proven wrong!) in the natural world of two similar geographical isolation events driving exactly the same species to evolve and both versions of the new species are more genetically similar to one another than they are to the origin species. The odds are just too slim even if to us the conditions seem identical.