An adverb for “up(wards)” derived from the root √AM “up” (PE17/157; Ety/AM²). In one place Tolkien said it “is generally limited to the qualification of words signifying or implying motion: especially ‘rise, ascend, climb, grow etc.’ (PE17/91)”, but that was not the case in (for example) Ambarussa “Top-russet” (PM/354), so this rule was not universal.
Conceptual Development: The Qenya Lexicon of the 1910s had ᴱQ. amu “up(wards)” reflecting the earliest form of the root ᴱ√AM(U) (QL/30), but by the 1920s it was amba “up” (PE13/137; PE16/62), a form that was retained thereafter. In one place in The Etymologies of the 1930s Tolkien gave it an alternate form ama beside amba (Ety/UNU), but since this was as an element in ᴹQ. amatikse “above dot” (Ety/TIK; EtyAC/UNU) I think it is more likely a variant of prefixal am- “up”.
An adjective or (pro)noun for “more” along with an adverbial form ambë derived from √AMA “addition, increase, plus” (PE17/91). These words were part of a (brief?) conceptual framework around 1967 in which the intensive prefix am- was derived from this root. Elsewhere the root √AM generally meant “up”, and Tolkien seems to have reverted to an-intensives by 1969 as evidenced by anírime “most beautiful” (PE23/133).
Neo-Quenya: Despite these conceptual changes, I think it is worth retaining amba and ambe “more”, perhaps based on ✱an-bā and ✱an-bē. The first of these would clash with amba “up”, but I think it could usually be distinguished by context: á anta amba nin “give more to me” vs. mennes amba i oron “he went up the mountain”. See √AMA for more discussion.