One of the biggest things I should note that if any private organization had such extensive ability to manipulate and create genetically modified organisms, that it undoubtedly would be under the watchful eye of any government with knowledge and or access to it, for the sole reason alone that it presents a unique opportunity for both industrial espionage (by competitors), as well as a bargaining chip. It would not be out of question that some of the science members, security teams, researchers and what have you are, in fact, also spies and reporting to one (or even more) agencies (or even nations) - some might even be providing this level of research to the highest bidder.

I would say some interesting elements to look at for this concept is "black projects" (high level secret operations at times conducted within normal projects, such as this, using the material and knowledge at hand without alerting the non-associated members), blackmail (a government or person using knowledge of this research as a means of blackmail, threatening along the lines of "If you don't give us exactly what we ask for, we turn this scenario around and reveal you're 'playing God' to the ever hysterical masses."), industrial espionage (stealing trade secrets with the intent to act on their own using mirrored or modified means), as well as the threat to societal norms.

Given this sort of research (as you've stated) is not socially acceptable, cloning a human being would undoubtedly create outrage - creating "perfect" humans more so, and to add another layer to human paranoia and fear, the notion of creating genetically enhanced humans (likely containing non-human material, making them "human chimera"). The sort of response you would look at, based on levels of offenses is anywhere from protests, social outrage, scrutinizing media, religious condemnation, wide spread hacking attempts (both private, foreign and government), as well as possible terrorist activities against facilities and persons associated with the project; this sort of topic has enough backing to get people outright killed by extremist groups if it was played out in a realistic scenario.

Another concern is the ethical element, namely for the possible non-human humans; they are, by virtue, largely human, but are they still human if their genetic material is not entirely all human? For example, an engineered human chimera is, by and large ninety-eight percent human, but the two remaining percent are stripped from animals (easiest and most efficient donors we have, as well as expressing countless desirable qualities), so the question is, are they still human? If yes, what about if they are forty-nine percent human, fifty-one percent something else?

Interesting story and concept, something I'd be willing to participate in as it is entirely my favored genre of modern, plausible science fiction.