Soup up is the phrasal verb meaning to modify something to increase its power, efficiency, or impressiveness. Soop up is a common misspelling, and supe up is a less common one (both soop and supe have rare senses that have nothing to do with increasing power or efficiency). Your spell check might tell you the inflected forms souped up and souping up are incorrect, but spell check is wrong.
Soup up originated in the U.S. in the late 19th century, though it wasn’t widely used until the 20th century. Its exact origins are unknown, but it could be short for supercharge, or it might come from a horse-racing slang term for injecting horses with narcotics meant to make them run faster.1 Through the middle decades of the 20th century, it usually applied to engines, but today souped up is used in all sorts of contexts.
In addition to the phrasal verb soup up, there is also the phrasal adjective souped up, which is hyphenated when it comes before what it modifies (e.g., a souped-up engine) and unhyphenated when it follows what it modifies (e.g., the engine was souped up).
Installed in 1964, it was the French government’s attempt to soup up what modernist critics then deemed an eyesore. [Wall Street Journal]
The record’s title track begins with an infectious hook, like a souped-up Ronettes with chunky electric guitars. [Spinner]
Dad helps five-year-old son soup up his plastic toy car with 66hp motor [Daily Mail]
But a recent encounter with a deliveryman on a bicycle that had been souped up with an electric motor … alerted me to the perils to pedestrians … [NYT City Room]
Short of running in some races for the sake of souping up your car, there aren’t any missions that actually revolve around vehicles. [Santa Rosa Press Democrat]