I'm writing a story about a genetically engineered human/alien hybrid race that was created by an advanced alien species. They were able to do this because earth and hundreds of other planets in the galaxy were seeded millions of years ago by an ancient progenitor species using their own DNA so although humans and these aliens were designed and evolved differently, they still share similar base DNA. 

Hybrids are possible, but only through genetic manipulation. Humans were built to be almost identical to the progenitor race so creating hybrids with humans is usually more successful than with other species. 

These particular hybrids were designed to be able to adapt in real-time to various different environments (eg, re-configuring their respiratory systems to function effectively in lower or higher oxygen environments), their DNA was also redesigned to be able to hybridize more effectively, eliminating the need for genetic manipulation to produce viable offspring between them and other races from the progenitor line. 

I'm just wondering if it makes sense or is biologically feasible for something like that to happen (bearing in mind that in this world matter manipulation exists and is relatively easy to do), and if it is, what is a good way to explain this that doesn't sound like Handwavium.