Used as a noun phrase meaning an additional item or instance. Often followed by a noun or used alone.
One more, please.
There is another problem.
Adverbial use meaning 'to an even greater degree'. Often used with adjectives or verbs to indicate a higher level than before.
Used in negative contexts to express that something is not quite satisfactory or falls short of expectations. Often appears as もう一つ～ない or もう一つだ.
See also: 今ひとつ
Today is even colder than yesterday.
His explanation made the problem even more complicated.
This dish is not quite flavorful enough.
His proposal is lacking something.
Variant using numeral 1; common in informal writing.
Combination of もう (already, more) and 一つ (one thing). The adverbial and negative senses developed from the idea of 'one more thing' needed to reach a satisfactory state.