Arnold has explained lucidly why splitting an infinitive is sometimes obligatory, as in "to more than double." But in the interest of historical accuracy (vulgarly known as "claiming credit"), I should point out that the observation, if not its elucidation, is first recorded in the usage note for "split infinitive" that I wrote for the third edition of the American Heritage Dictionary, which appeared in 1993. It reads, in part:
In We expect our output to more than double in a year, the phrase more than is intrinsic to the sense of the infinitive phrase, though the split infinitive could be avoided by use of another phrase, such as to increase by more than 100 percent.
I'm less than happy with that phrase "intrinsic to the sense of the infinitive phrase," and to tell the truth I can't recall why I used it, though in writing these notes it's always difficult to come up with an explanation that's consistent with the limits of readers' grammatical sophistication and the requirements of brevity. In any case, when we polled the dictionary's usage panel on that example, 87 percent of them found it acceptable, though I suppose you could say that the fact that fully 13 percent demurred is evidence of just how strong a hold these superstitions have on some people.