Graduation speakers burned out on Rudyard Kipling’s “If” will soon have some fresh options, thanks to a trove of newly discovered Kipling verse to be published for the first time next month. The three-volume “Cambridge Edition of the Poems of Rudyard Kipling,” edited by Thomas Pinney and released in the United States on March 31, will include more than 50 poems uncovered by Mr. Pinney in recent years, including several found in the papers of a former head of the Cunard cruise line and one discovered during the renovation of a Manhattan townhouse, according to a statement from Cambridge University Press. The newly discovered poems include comic verse written during a crossing from Adelaide, Australia, to Sri Lanka (and most likely read aloud to passengers), an 1889 salvo against media intrusion called “The Press” and a Christmas poem called “Across Our Northern Uplands,” written after Kipling had moved to Vermont and “was still full of enthusiasm about life in America,” as the press put it. The Cambridge edition, billed as the first complete edition of Kipling’s verse, includes more than 500 previously uncollected poems, with perhaps more to come. “There is a treasure trove of uncollected unpublished and unidentified work out there,” Mr. Pinney, an emeritus professor of English at Pomona College, said in the statement. “I discovered another unrecorded item only recently and that sort of thing will keep happening.” Mr. Pinney also predicted a resurgence in the scholarly fortunes of Kipling, who, thanks to such poems as “The White Man’s Burden,” has often been dismissed as an apologist for British imperialism. “Kipling has long been neglected by scholars probably for political reasons,” he said.