If these were nouns, I would assume "single" fits in between:
1/4, 1/3, 1/2, 1, 2, 3, 4 . . .
quarter, third, half, single or one, double, triple, quadruple . . .
Note that each word has a cardinal as part of its etymology: quarter evolved from the Latin quattuor ("four"), double from Latin duplus (“twofold”), and so on.
However, in the case of verbs, is there a word to indicate multiplying (or dividing) by one that fits into this pattern? The closest I can think of is unify, "cause to become one", but it wouldn't make sense in context:
She doubled the number, i.e. multiplied by two.
She unified the number, i.e. multiplied by one.
The word wouldn't necessarily have to have the mono- or uni- prefix, but the etymological root ought to contain the cardinal for one (i.e. "she maintained the number" wouldn't work) in keeping with the pattern.
Best Answer
I'm not aware of a satisfactory verb for the question's purpose. There are several nouns corresponding to the unit multiplier, such as unit, in sense 2, “The number one”. Note that the more-specialized sense 10, “(algebra) An element of a ring having a multiplicative inverse. (Formerly just the identity element 1R of a ring.)”, would in some rings include just the units 1 and -1, but in others may include numerous other values with magnitudes other than 1. Term unity, in sense 1 is “Oneness; the state or fact of being one undivided entity”, and in sense 4 is “(mathematics) Any element of a set or field that behaves under a given operation as the number 1 behaves under multiplication.” Term identity in senses 5 and 6 is “(algebra, computing) Any function which maps all elements of its domain to themselves” and “(algebra) An element of an algebraic structure which, when applied to another element under an operation in that structure, yields this, second element.”
For verbs, there is the rather clumsy identity mapping; one could say “she identity-mapped (or unity-mapped) her investment in (or to) profits”, which ought to mean 100% ROI, but whether it would be understood as such, or as gibberish, one hesitates to say.