A multicompany example with Red Sonja. Kulan Gath was created by Marvel comics for Conan the Barbarian's ongoing (specifically Michael Moorcock of all people). However, he would go on to become Red Sonja's archenemy in both Marvel as well as Dynamite.
In Sonic the Hedgehog (Archie Comics) series, the Dark Legion - a group of villainous Echidnas - was originally created to serve as enemies of Knuckles, acting as the central antagonists of his spin-off. However, after the "Enerjak Reborn" arc in the main series (several years after the Knuckles spin-off was cancelled), the Legion allied with Sonic's Arch-Enemy Dr. Eggman and began serving as his personal army. Therefore, they can be seen as much Sonic and the Freedom Fighters' enemies as Knuckles'.
Done intentionally in The Great Fables Crossover in which Snow White and Bigby Wolf deal with Literals, antagonists of Fables spin-off series Jack of Fables, while Jack, who clashed with them all the time until this point, doesn't move a finger to help.
Pete is usually depicted as the Arch-Enemy of Mickey in the comics from the beginning - but especially in older comics Pete would ocassionally appear in Duck comics as either a rival to Donald or threatening Scrooge.
Emil Eagle originally was made up to give Gyro Gearloose a criminal rival, but he later became a recurring character in Mickey Mouse comics by Paul Murry et al., mostly to explain how people like Idget the Midget and Dangerous Dan McBoo or Pete could have sophisticated plans or super-science equipment; recent Italian stories put him as Super Goof's opponent in a relationship akin to Superman and Lex Luthor.
The Beagle Boys and John Rockerduck are usually Scrooge's villains, but they also have to deal with Paperinik (Donald's superhero identity), and the Beagle Boys are also enemies of the Red Bat (Fethry's superhero identity). The Beagle Boys also would show up as opponents in some old Super Goof stories. Here, they are often portrayed just as regular crooks.
The Phantom Blot is mainly Mickey's foe, but has scuffled with others from time to time.
Ultraheroes has this in spades, with the heroes mostly 'borrowing' their rivals from Paperinik. The main exception is Paperinika (Daisy's super hero alter ego), as she already had it personal with Sapphire.
Darkwing Duck features several Duck comics and DuckTales villains such as Phantom Blot, John D. Rockerduck and Magica de Spell.
Petey the Cat made his debut in Super Diaper Baby 2: The Invasion of the Potty Snatchers, but he is far better known for being in the Dog Man series.
Transformers comics had, across several separate continuities, stories in which G.I. Joe villain Serpentor is somehow involved, usually with him transferring his mind to a robot body and becoming a threat to Cybertronians, sometimes even becoming a recurring character.
General Tara was an enemy of The Phantom, but his Legenderry counterpart is the military dictator of Zorro's homeland. Since he only appears as part of a Legion of Doom which both Phantom and Zorro oppose, this doesn't make a huge difference. Dr Moreau is also a member of the Legion, but the heroes do not included a version of Prendick.
