Question: Kind of a "universal donor" or "universal recipient"? Aliens that can take on the qualities of several kinds of species and recombine them to make a kind of "super" being?

Answer: 
"Is it plausible that there could be an alien species that has the capacity to mate with and share genetic material with many other alien species?"

No. Biology doesn't work like that. A human-Vulcan hybrid like Mr Spock couldn't arise via normal reproductive mating, but it could happen via biotechnology assisted reproduction. Fairly advanced biotechnology, but it's not inconceivable.

"Kind of a "universal donor" or "universal recipient"? Aliens that can take on the qualities of several kinds of species and recombine them to make a kind of "super" being?"

Again no. But again this could happen via genetic technologies whereby genes can be shared (assuming the alien species involved have reasonably compatible molecular biology or, as we used to call it biochemistry).

Genetic hybrids already exist and current genetic engineering techniques can make them. Aliens with advanced technology could carry this process to the nth degree. They could make some interesting recombinant organisms. These could be better adapted to a wide range of environments. But could this lead to making a "super" being? Very doubtful. The concept of a "super" being is a mirage at best.
On its own, no.
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* Genetic material is not compatible. DNA is not compatible with structures of not only different chemicals, as would likely be present, but also different, non-helix shapes, making the combination of genetic structures **extremely improbable if not statistically impossible**.
* If the genetic material is somehow adapted by exchanging most of the molecules for compatible chemicals, and changing the shape (which your organism, however complex, probably cannot do), the genes produced will not have the same meaning to decoding enzymes or machines. What may mean blue eyes for species A could be decoded as an exoskeleton for species B.
* If you make the genetic molecules compatible, and make sure the genes represent what they are supposed to do, the offspring will likely be grotesque and
malformed. Cross a human and a cow and you will **not** get
a cow with a human head or a human with udders. Things will mix in a
number of unpredictable ways and kill the organism. Picture a human with a compartmentalized stomach, fur, a skewed metabolism, and a circulatory system that doesn't go through the entire body, effectively killing the creature at birth.
* If the body somehow functions, which is **very very unlikely**, the brain still probably won't. It will not have regions corresponding to every organ in the body, as a random combination of genes means not every organ gets representation. Additionally, it may have redundant regions that evolved to control something that this hybrid creature doesn't have.
* Finally, if all of the above conditions are met, and through impossible statistics, the organism is able to develop and survive, it will die in utero. The mother organism will create the child using the nutrients it knows how to process for *its own kind.* It will not process the nutrients the other organism inside of it needs to grow effectively.

However, complex machines can always solve your problems.
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