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.