Yes. But only within limits, and with assistance.
We already have the ability to transfer genes between species. This is how we manufacture the bulk of our insulin: we created bacteria with literal human insulin-producing DNA spliced in. And, sure, maybe this resulted in some negative side-effects for the bacteria, but we didn't care about that--so long as the process worked, and allowed us to produce human-compatible insulin in commercial quantities, that was all that mattered.
CRISPR, a newer technology, allows us to do this with even greater precision. So as long as you accept the side-effects, it can theoretically transfer a wide range of genes--and their accompanying traits--between species.
Limits
Obviously, using any sort of DNA-alteration to alter a species is going to have limits. Even if we identified the "eye-producing genes" from a human (which is itself a more vague classification than you might think,) trying to splice those into a bacteria isn't going to wind up with single-cell organisms with microscopic eyes on them, visually observing the world around them. There are far more elements needed to produce, sustain and make use of a functional eyeball than just those of the eyeball itself. Some species are simply too different to swap the bulk of their traits; and even very similar species will have enough differences to limit their inter-compatibility. (And this is even not worrying about the fact that once you have the appropriately-modified DNA, the changes might be such that no living creature can successfully gestate the unborn child.)
A good portion of the problem is that, without knowing the limits ahead of time, it will take a good deal of time, resources and effort (not to mention unethical experimentation) to uncover them. Only once those are known could one even begin to find a suitable solution to their search for a viable chimeric combination.
Assistance
This is where the assistance comes in, and, even though I suspect we'll see a growing number of answers to technical issues (fictional or real) default to this in the common years, it's not just because it's trendy, but because it actually works: AI will be the path forward.
Large language models (LLMs) can now pass the Turing test often enough to be considered usable for numerous purposes (witness the explosion of ChatGPT apps.) And these are systems where no one explained sentence structure, or nouns vs. verbs to them... they deciphered all of that on their own, to the degree that they can literally converse well enough to fool humans, all by examining the statistical relations between words from enough textual sources. That's it. And we know that with enough data, training time and processing power, the number and quality of inferences and connections they can make only increases, up to and even beyond the abilities of most intelligent people.
So if someone were to, say, have done nothing but experiment with DNA and CRISPR on multiple species for years, even decades, recording all the results in a structured format, and used that as the training data for even a straightforward LLM, then the only thing that would stop that system from being able to tell you PRECISELY what genes you would need to transfer, and from which creatures, to get specific effects, and to tell you what side-effects you could expect (and possibly how to minimize or counter them,) would be (1) the quantity and quality of the experimental data, and (2) technical resources.
It's actually a bit frightening that this is actually on the table now, in the real world.
So, yes, with a powerful enough, properly-trained AI assisting (possibly armed with the research of an villain who's been doing dark experiments for a decade,) it is indeed possible to use a technology such as CRISPR to swap genes into human DNA to transfer traits and produce numerous different approximations of what could be called a "super-soldier."
You probably won't get one with bat ears or an elephant trunk, but hybrids with a selection of more-subtle traits that add up to a notable battlefield advantage would definitely be possible.
Of course, whether this would be economically viable, or whether the side-effects produced in the resultant chimeric humans would be significant enough to cause issues, is another question entirely.