In modern commercial fiction, the "logic" of crossovers is always the same. The crossover may be engineered in any number of ways:
(1) by a single author who decides to have characters from distinct storylines meet one another, as one sees in Rider Haggard's 1921 novel SHE AND ALLAN, which brings about a meeting between She-Who-Must-Be-Obeyed and Allan Quatermain;
(2) by an author (or authors) who brings together characters in public domain, as one sees in the Alan Moore-Kevin O'Neill comic-book series LEAGUE OF EXTRAORDINARY GENTLEMEN, which associates the aforementioned Quatermain, Jules Verne's Captain Nemo, Robert Louis Stevenson's Mister Hyde, and many many others.
(3) by a company who owns from inception, or purchases from another corporate entity, a group of characters whom that company then chooses to associate with one another. (Said companies may also choose to include public-domain characters within their modern-day mythologies: the comic book companies Marvel and DC both gave rise to versions of the archaic hero Hercules who then became entangled with each company's modern-day superheroes.)
There may be other variations of this process, but the logic is always the same: to intrigue readers/viewers so that they will patronize not only the crossover-work, but also any and all works that gave rise to the crossover. The practice is most associated with-- but is not limited to-- the merchandising of ongoing serials, and can often be used for the process of using a well-known series to "hype" one that is less well-known by the target audience. When Edgar Rice Burroughs wrote his 1930 novel TARZAN AT THE EARTH'S CORE, the character of Tarzan was already world-famous. Did that crossover help the sales of the books in the "Pellucidar series," where Burroughs originated his "land at the center of the earth" concept? I don't know, but the possibility of making that series more popular probably crossed Burroughs' mind before he wrote the crossover.
Some Marxist critics will view such character-crossovers as one of many strategies by which the evil Masters of Mass Culture manipulate their audiences. While such explanations may seem to answer all questions as to the motives of the stories' producers, they don't say anything substantive about why the audiences choose to patronize not just works of mass culture in general, but works in which characters or concepts from different storylines happen to intersect. The usual Marxist explanation is that these audiences want nothing more than mindless divertissement. However, the overlapping of distinct storylines would seem to intensify the degree of mental effort an audience-member must exert in order to participate in the crossover's intersecting universes. For instance, when Rider Haggard takes a character who exists in a moderately realistic universe, i.e., Allan Quatermain, and causes him to encounter a character whose nature is overtly supernatural, Haggard must find some way to treat both characters with integrity, even though the ground rules of their universes are in conflict. I'll discuss this particular example in more depth in an essay devoted to this novel.
It's something of a given in literary criticism to state that audiences, literary or sub-literary, maintain interest in fictional characters by identifying with them. This commonplace observation is not so much wrong as overly simple. As I am what has been called a "myth-critic," I assert that the process of identification comes about as a reader (or viewer) realizes what kind of role the character plays in the story, and what that fictional role means to the reader. This does not mean "identification" in the simple-minded sense of "I want to be like this person," for identification can take place with any number of villains (the Joker, Freddy Krueger), monsters (Godzilla) or even mysterious locales (the subterranean domain of Jules Verne's "Center of the Earth.") It is more properly an appreciation of what I will call the "mana" appropriate to the character or concept's role in the story.
A crossover features at least two characters who have established-- or will establish-- the "mana" that has or might make them popular. In the above example, She-Who-Must-Be-Obeyed has one type of "mana," while Quatermain has a different type. It is this "clash of energies" that I believe readers enjoy in crossovers, a clash that is radically different from the normative encounters of a hero and his villains.
Two more points:
First, I was careful to say above "characters who will establish" their mana because some of the crossovers I'll talk about here are what professionals term "spin-offs." Burroughs' "Pellucidar" novels had already been launched prior to the Tarzan-Pellucidar crossover, so "Pellicidar" was not a "spin-off" of Tarzan. However, it's possible for a company to launch a franchise that it hopes to make popular, through association with a successful franchise. The television medium is particularly known for what are called "back-door pilots," in which characters for a franchise not-yet-launched are introduced on an established series.
A couple of the crossovers I'll discuss here qualify as "back-door pilots," as with the episode in which the main character of the Norman Lear franchise MAUDE guested on a 1971 episode of Lear's successful ALL IN THE FAMILY sitcom, before the character and her entourage appeared in their 1972 program.
However, I disallow any and all "back-door pilots" which did not eventuate in a series, as is the case with the STAR TREK episode, "Assignment Earth." I also disallow parodies which may blend together two or more characters who are parodic versions of franchise characters, as is seen in Philip Jose Farmer's story "Showdown at Shootout," which includes travesty-versions of the Shadow, Doc Savage, Fu Manchu and others.
Second, I'll frankly admit that the majority of these crossovers are taken from comic books. There are various reasons as to why this medium is so prominent in the history of pop-fiction crossovers, reasons that would require a separate essay. But even in admitting the comic-book medium's pre-eminence in this regard, I will exclude one type of "crossover" that Jess Nevins mentions in his essay on the topic. In contrast to Nevins, I don't regard "hero-teams" as genuine crossovers. They resemble what I've termed the "static crossover." However, in my opinion a series devoted to the teaming-up of characters with their own separate mythoi is not just "static," but "regularized." From the first appearance of the Justice Society within the same story in ALL-STAR COMICS #3, there is no longer special attention to the unusual nature of the crossover, simply because it is the main appeal of an ongoing feature. This type of "crossover" I will not explore.