Can any organism possibly have the capability to create a new species every time it reproduces?
Concept of species

First have a look at How could humans have interbred with Neanderthals if we're a different species? to better understand the concept of species.

I will assume that you are using the "biological species definition" which is based on reproductive isolation.


  Can any organism possibly have the capability to create a new species every time it reproduces?


The question is mainly non-sense. In short, if it is true that all offspring are a new species, it means that by definition the lineage is asexual and then the concept of species is typically considered to be of little interest. Let's consider both asexual and sexual lineages separately to maybe clarify what I mean.

Asexual lineages

For exclusively asexually reproducing lineages, either we decide the question makes no sense because the concept of species does not apply to them. Or we decide the concept of species applies and then every individual is necessarily a new species. So, yes, by definition there is no exclusively asexually reproducing lineages where a new species isn't created at every reproductive event.

Sexual lineages

For sexual lineages, the question would make no sense either as if it was the case that every individual was it's own species, then the lineage would be asexual!