Edwin Sachs described a multiple shift in Sleight of Hand, 1877, p. 96. It was a secret maneuver, much like a traditional pass.
The first instance of the modern approach using an outward Hindu shuffle action was recorded by Dr. Jacob Daley in his notebooks under the title “Four Ace Bevel Push,” and invented by him in the 1930s, as can be seen in Jacob Daley's Notebooks, n.d. (c. 1974), n.p. (Item 334). A reconstruction of Daley's sleight, made from his four-line note, is done by Karl Fulves in Epilogue, No. 13, Nov. 1971, p. 102. Ed Marlo reinvented the basic principle in his single-card push-in Ace control, in Marlo in Spades, 1947, p. 7, which he later renamed the spade multiple shift in his Multiple Shift, 1961, p. 2. The first multiple shift to be published was Dai Vernon's, in Arthur Buckley's Card Control, 1946, p. 20. Vernon is on record as saying his starting point was Jack McMillan's Plunger Principle.
Also see: D'Amico Multiple Shift.