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: 
Sorta yes. It may be possible, but not likely.

One issue is that we don't know if all life would be the same handedness. There is no reason it should be, in fact it should be about 50/50. How much the handedness of compounds matter can range from not mattering at all to being very potent toxins where if you expose someone to a compound that is left handed it will really be beneficial, but if its right handed it will kill them instantly.

But let's say all life works on basically the same RNA/DNA system. Well, then you're pretty much down to the programming analogy. Basically, there is no reason for some 4 bits to be one command and another be a different one. You're just randomly asigning them, but all PCs can run most OSs because they all use roughly the same base level command structure. Assuming there is limited amount of options for what those biological commands are (which as faras I can tell that is the case) then it should be possible to give birth to a given species by alien species (ignoring other issues). As in if bob the human mated with Susan the martian, susan could give birth to a human, but she could not give birth to Human-Martian hybrid from just this, because the commands are only for a human or a martian, not both. 1 BIOS can run at a time and 1 OS can run at a time...

So how do you get a hybrid? Shells. You can run a shell program which allows you to run another BIOS/OS on the same computer while running the main OS. The Shell OS can make alteration to the files and such just as the main OS, but the main OS is in charge and also you are expending more resources to run both. Is this possible with biology? I see no reason why not.

So you'd then get a hybrid Martian-Human, but the Martian would be dominant to the point where you might as well not call it a hybrid.

The alien from the movie Species and the Asari from Mass Effect both seem to work in outward appearance similar to this.
"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.