In An Intergalactic Puzzlepalooza you control the five aliens Dinko, Gumpers, Flip, Swanky and Scruffy. They all have their special abilities, and the purpose of the game is to utilize these abilities in order to obtain certain gems that lie scattered around various levels. The player starts out controlling Gumpers, and as the player progresses throughout the game, the other aliens become unlocked.
The game centers around five aliens and their quest to save their Earthling friend Tommy Cadle. The aliens and Tommy Cadle are taken into space in Robotix's space ship, where the aliens have to overcome numerous obstacles in order to save their friend.
Source: Wikipedia, "Pet Alien: An Intergalactic Puzzlepalooza", available under the CC-BY-SA License.