In my idea for a WB Fighting Game, a lot of different franchises cross over with each other. To me, crossovers only work if it makes sense for the different franchises to meet each other.
Looney Tunes, Tiny Toons and Animaniacs debatably take place in the same universe. Proof of this? The Warners cameoed in Spring Break Special and Fifi wore a Dot Warner costume for Halloween. More examples appear in the form of Elmyra
She was shoehorned into every WB Cartoon in the 90s and singlehandedly ruined Pinky and the Brain.
Freakazoid resides in a universe that's populated mostly by humans, like our world. However, Wakko and Brain made a memorable cameo appearance, and Freakazoid attended the Big Wrap Party. Besides, that show is known for its random humour.
Characters from Hanna-Barbera such as Tom & Jerry, Scooby-Doo, Hong Kong Phooey and Captain Caveman appear because they're pretty much owned by WB now. They're mentioned in Slappy's monologues (such as George Jetson being the ex-boyfriend of Bumbie's Mom) and Hamton dressed up as Barney Rubble for Halloween.
The Justice League, as we all know, has been parodied by TTA in the form of the Just-Us League. The Joker sang "Smile, Darn Ya, Smile", which was a Looney Tunes song, and the DC Superheroes have been in LEGO games as well as the Movie, which is where Emmet Brickowski comes in.
Harry Potter, Dumbledore, Voldemort and Gandalf appear because, like the Justice League, they have also appeared in LEGO games. Another reason to justify their appearance is the fact that Shaggy and Scooby are playable in LEGO Dimensions.
The Grinch was written by Dr Seuss, who also wrote some of the dialogue in the Private SNAFU shorts. In the 1960s, Chuck Jones made an animated adaptation of "How the Grinch Stole Christmas" which has become a beloved classic. Private SNAFU's shorts were directed by Looney Tunes directors and the eponymous protagonist was voiced by Mel Blanc. Bugs also made cameos in the shorts, which was lampshaded in his Technical Fairy Conversation.
Or...if you want to have a less complicated explanation, just check out Who Framed Roger Rabbit and use that principle.
If you want to see a crossover that had potential, but squandered it...check out Playstation Move Heroes.