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.
... I'm pretty sure there is an organism (not sure if single-celled or multi-cellular... though single-celled is more likely) which 'borrows' DNA from other organisms to add genetic variation & abilities due to being asexual reproducers. (From a quick google search i found that i might be referencing bdelloid's as they have this behaviour). 

So it is possible to take genetic information from other organisms and use it to reproduce, the problem lies in whether your aliens have DNA/RNA or if their genetic code is compatible with other organisms. 

I hope this answers your query.