EVENTUALLY.
Seriously, I cannot stress that enough. This isn't something that needs to be done, if it's going to be done, soon. As more species are added, perhaps this feature could be added as well. in the future. Maybe it's even planned already, who knows.

Certain mythological creatures either are or easily could be a combination of other magical creatures. For example, a hippogriff is said to be the offspring of a gryphon and a horse. We don't have horses but we do have unicorns.
There are many others, since most mythological animals are a mix of different ones, but I'll leave that interpretation open to Angel if she wants to add something like this in the future.

Not all mixed breedings would result in a new species, in fact most would just fail outright. Only certain species can crossbreed successfully for a variety of reasons.
For example trying to breed a roc and a unicorn to get a hippogriff would always fail because a) rocs are freaking huge and incompatible with unicorns and b) just because it's a bird/horse creature doesn't mean it's made by breeding a bird and a horse, it's a distinct combination of genes required to get the species.

Even species that look like a combination of other species may also be their own distinct species and cannot be made by cross-breeding. For example gryphons could be their own species, not hybrids, breeding a puma with any bird would never result in a gryphon for this reason. Just because they look like a mix doesn't mean they are.

I would say, for balance reasons and just how unlikely it would be for the two species to come together in the first place, both would need full 10/10 energy for the breeding. Whether it's successful or not, would deplete energy entirely. Even if the species does have a "hybrid" that can be made by breeding them there is still at least a 50% chance of failure.

Genes could either be assigned randomly or based on the equivalent parents' genes. Because magic, how's that for an explanation?

Hybrids could occur naturally too, but extremely rarely.

Support for the general idea, but no support for complete energy depletion. How about half energy depletion?

No support. This is just making this unnessecarily complicated. Why not just make a hippogryph species on its own?

Some of that is a little overcomplicated, but hybrids are always cool. 

I personally love the idea... I have an over abundance of females and would love to be able to breed things together... I mean a dragon-unicorn? How cool is that?

Hehe... Not sure I can see a roc and a cockatrice... well... you know.. yeah...

So for that reason I think maybe this could be a feature found in the laboratory- less breeding. You can only create a hybrid though some sort of invetro and both parents must have 10/10 energy, it could possibly fail, and I don't know whether or not I think the restulting offspring should be able to breed (if so it would have to be watered back down into one of the parent's breeds)... or something like Khimeros... I dunno... I lost my train of thought and it is late at night...

Good idea, but I think it needs some.....improvement.

Absolutely ShadowClaw, feel free to add anything or suggest any changes you want. This is just an idea for the distant future, provided Angel wants to do anything like this. Not my site, just brainstorming.

No support, I'd rather keep species within themselves. All of the gene crossing, the oddly-appearing lineages and the concept behind it isn't really something that I'd like to see here.

maybe instead of hybirdism just make it to where certain species have a breeding compatibility.  like a tiger and lion can geneticly breed together.
 the difference if applied to BK would be that the offspring would just be one or the other breed. (or which ever breed the mother was if you want a little control)

basicy

a dragon x cocktriace

cok x roc

puma x gryff

gryff x roc

the poor uni would be left out of the pool till a pegasus is possible added

It does sound a bit like Khimeros. Not sure if support. More species are always fun, though.

"the difference if applied to BK would be that the offspring would just be one or the other breed. (or which ever breed the mother was if you want a little control) "

^ This reminds me of Greek mythology and what the offspring of nymphs would be. Like, if they had a child with a satyr and it was male, it would also be a satyr, and if female - a nymph. Likewise, if the father was human - then either human or nymph.