is there a way to determine if 2 species of cory can crossbreed
Yes.
Taxonomy involves the relationships of species, and those descended from the same ancestor species are deemed to be a lineage, or clade. A distinct lineage is classified as a genus, the first name of the two name (binomial) classification used for all life. The species in a genus therefore have the closest relationship and are more likely to hybridize. But this depends upon circumstances, and before going into that there is another factor that needs to be considered with respect to the genus.
Above I noted that a lineage is a group of species that all descended from the same ancestor species, and in such cases the clade/lineage/genus is termed monophyletic. The genus
Corydoras is polyphyletic, which means that the species now classified in this genus descended from more than one ancestor. Nine lineages within the present genus have been identified, and no one doubts this because every phylogenetic analysis to date has confirmed it. Eventually there will be nine distinct genera in the family Corydoradinae; one will be
Corydoras, but the vast majority of the 465 known species will be in a different genus from the true
Corydoras species.
Aspidoras is within this classification (lineage 2), and
Scleromystax (lineage 3), and the three former
Brochis species are in subclade 1 of lineage 8.
So, to the question of cross-breeding...Ian Fuller has noted that
Corydoras species within the same lineage that are maintained in decent-sized groups of each species with both genders present are much less likely to cross-breed because their natural instincts lead them to spawn with their own species if male and female are present. The hybridization is much more likely to occur if one species has only males or only females, and the other species in that lineage has the opposite gender. I have certainly had this occur in my tank of cories, where a female (on her own due to last survivor) has spawned with a male of another species which happened to be one of two males of that species in the tank. But you do not want to encourage this, so maintaining decent-sized groups (including male and female in numbers) of each species should prevent hybridization, though nothing is ever cut and dried. Keeping the species separated, i.e., only one species to a tank, is obviously the safest course of action.
I can further explain any of this if asked, or why hybridization is not encouraged but is adamantly opposed by biologists.
