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We have seen plenty of examples of Earthlings (Terrans) who have obtained superpowers through various means:

• Bruce Banner, became the Hulk after exposure to Gamma Radiation


• Steve Rogers, gained super-human strength and abilities from a super-soldier serum


• Inhumans, obtain superpowers through Kree (alien) interference

Have there been any aliens who have obtained superpowers via similar means? I'm not talking about aliens like Asgardians, Kree, Skrulls, etc who are naturally stronger and more resilient than Humans. I'm referring to any extra-terrestrial beings (of commensurate composition with Humans) that have been exposed to anything that left them with powers that others of their race would consider "super".

Answers from both the MCU and Comics are acceptable!

I can think of three immediate examples:

• Super-Skrull, a Skrull warrior, was given (through some means available to Skrulls) the combined powers of the Fantastic Four. https://en.wikipedia.org/wiki/Super-Skrull
  


• Silver Surfer, from Zenn-La, was given the Power Cosmic by Galactus (and by implication every non-human Herald). https://en.wikipedia.org/wiki/Silver_Surfer
  


• Beta Ray Bill, a Korbinite, was given the Power of Thor. https://en.wikipedia.org/wiki/Beta_Ray_Bill
  

Beta Ray Bill is a Korbinite (alien from the planet Korbin) whose:

life force and consciousness were transferred by scientists of his race into the body of an alien carnivorous equine-like beast that had been bionically restructured into a cyborg. Courtesy of highly advanced genetic engineering, the character possesses vast superhuman strength, speed, stamina and durability, and a highly extended lifespan.

Bill was also notable for his worthiness to wield Thor's hammer Mjolnir.

Bill was also depicted in statue form in the MCU in Thor: Ragnarok.

Kallark is a Strontian individual who went through an enhancement process which massively improved his already impressive physical abilities to become Gladiator, Praetor of the Shi'ar Imperial Guard.

Speaking of the Shi'ar, Deathbird was a Shi'ar who was born with a form of atavism, which gave her claws and allowed her to fly.

I think that the best examples would be the Shi'ar Imperial Guard, made up of super-powered beings from many different planets (even Earth). They are lead by Gladiator, the last Strontian.

More examples would be from the Kree Starforce, who are super-powered above and beyond other Kree. Among them was Ultimus, an Eternal.

There are also the spaceknights of Galador. Most notable among them would be Rom.

Galactus grants the power cosmic to his heralds, most of whom were not from Earth. Among them were:

• 
  Stardust, an Ethereal


• Morg


• 
  Terrax, a Birjan aka Landlak.


• Firelord


• Air-Walker


• Tyrant

As mentioned in other answers, the Super Skrull and Beta Ray Bill would also be excellent examples.

The Elders of the Universe

The Elders of Universe are probably the closest thing to what you want; they are a group of individuals, each belonging to a separate alien race. All other members of their races are extinct, and so they consider one another brothers, though none are related (except Voyager, who is related to the Grandmaster). Each one possesses immortality. I can't remember how each one gained immortality, but it stands to reason the rest of their races didn't, as they are extinct, after all. Later, the Grandmaster won complete immortality for all the Elders after beating Death in a game. They all have different powers; the only one they share, to my knowledge, is immortality and maybe super-strength.

The Elders of the Universe first began calling themselves such sometime before the Earth was formed, meaning their races were spacefaring long before anyone else, except the Celestials (obviously) and most likely the Watchers, Builders, and Progenitors. They are generally neutral or evil, in terms of behavior towards Earth's heroes, and they are most famous for: keeping the Infinity Gems during the Thanos Quest, for the Grandmaster repeatedly playing games involving Earth's heroes, for the Thing and She-Hulk beating up the Champion, and for the Collector, who has collected some crazy stuff over the years, including Earth-1610's Mjolnir.