No that's not a typo in the title! Willoughby Sharp was scheduled to produce a third detective novel in 1935, The Mystery of the Multiplying Mules. It would have been the second Sharp novel, after Murder of the Honest Broker, to feature Inspector Bullock. A short description of the book was actually given in promotional material.
Here is the description:
Inspector Bullock is called in by the Logans not because something has been
stolen, but because something has been added to their household. On three
successive Friday mornings they have found in their locked barn, mingling with
their own animals, two strange mules. Before the reason for the multiplying
mules is found, three deaths follow in rapid order.
Maybe we'll get lucky and this will turn up somewhere. It's odd that it was never published, when they got this far with it. Interestingly, Kirke Mechem, whose 1936 novel The Strawstack Murder Case (A Frame for Murder) was reprinted by Coachwhip recently, also has a "lost" mystery novel, one that was turned down by his publisher, Dodd, Mead, his son, the composer Kirke Mechem, tells me, because it dealt with "miscegenation" and was then shelved by the author.
Here's hoping those mules turn up again!