People sometimes use one or the other of two expressions from Charles Dodgson—"through the looking glass" and "down the rabbit hole"—to indicate "ridiculously or mind-bendingly off the rails" or "departing reality and entering fantasyland," either of which meanings has some elements in common with the sense of "jump the shark" as it is broadly used.
For example, from an unidentified article in The Economist from October 18, 1958 [combined snippets]:
Yet the policy which Mr Amory appeared to be adumbrating at Blackpool to some extent went through the looking glass compared with the general forecast. The impression left with most of his audience was that Mr Amory may go on living down to his — hitherto admirable - nickname of Derick-or-little-by-little this winter (when industrial capacity may be unnecessarily under-utilised), but that he hopes to give a lot of money away next spring in time to restimulate activity later in 1959 (when things might conceivably be getting less disinflationary on their own).
And from "Responses to Questions Asked by Senator Lloyd Bentsen for Response by Waste Management, Inc. Concerning Ocean Incineration" (July 9, 1985), in Ocean Incineration: Hearings Before the [U.S. Senate] Subcommittee on Environmental Pollution of the Committee on Environment and Public Works (1985):
The Coalition witness went through the looking glass in describing a workshop held in June 1984:
A regulation development workshop was held in June of 1984. Representatives from the Attorney Generals' offices of three states and numerous environmental groups were invited to provide input. Prior to the meeting, a fully developed set of regulations leaked to the opposition participants. When the EPA officials were confronted with the document, they denied any knowledge of its existence.
During the rather emotional revelation, a member of industry leaped to his feet and was overheard exclaiming, "That's a privileged document. Only industry is supposed to have it." Senate Hearing Transcript at 50.
CWM representatives were present throughout this meeting. To our knowledge no advance copy of draft proposed regulations was leaked to any industry representatives. CWM had no advance copy prior to that meeting.
From an unidentified article in Newsweek magazine from 1988 [snippet view]:
Douglas Ginsburg's Supreme Court prospects went down the rabbit hole after someone remembered his youthful experiments with pot. No one was entirely prepared for this blood sport.
And from Rafael Alvarez & David Simon, The Wire: Truth Be Told (2004/2009):
"I {tried to} make him [Omar] believable by playing him from a sensitive perspective, not just as an alpha male. I played him very vulnerable. When you hurt Omar's feelings, he acts a certain way," said [Micheal] Williams.
"In Season One he was happy and in love with Brandon. Then he went into a dark depression when they killed Brandon. He fell in love again in Season Four but went down the rabbit hole after they killed {his confidant} Butchie.
I would caution however, that "jump the shark" has a TV trope sense in which it may apply specifically to "a program that was formerly of high quality but now has become unwatchably absurd." Broadened beyond the context of television, that sense of the expression might find its best traditional equivalent in "gone to pot." Christine Ammer, The American Heritage Dictionary of Idioms, second edition (2013) offers this entry for that expression:
go to pot Also go to the dogs. Deteriorate, decline; come to a bad end. For example, My lawn has gone to pot during the drought, or The city schools are going to the dogs. The first of these expressions dates from the late 1500s and alludes to inferior pieces of meat being cut up for the stewpot. The second, from the 1600s, alludes to the traditional view of dogs as inferior creatures.
