This is the 190th most frequent Japanese word.
もっと
"More" or "even more."
Here, 'もっと' conveys the meaning of 'more' in the context of quantity, specifying the request to add more sugar than already present.
もっと砂糖を入れてもいいですか？
May I put in more sugar?
In this example, 'もっと' modifies '早く' (earlier), emphasizing the degree of earliness, thereby expressing regret about not leaving significantly earlier.
もっと早く家を出るべきだった。
I should have left the house earlier.
In this sentence, 'もっと' means 'more' or 'to a greater extent', modifying the verb '勉強しなければなりません' (must study) to indicate the necessity of working harder than currently.