あくまでも + [noun] + だ/です あくまでも + [verb]
あくまでも is the longer form of あくまで and means the same, with a little more weight. Both can be written あくまで飽くまで, but kana is the usual spelling. Before a noun and だ or です it limits how a statement should be taken: "only X, nothing more". Before a verb of insisting or holding on, it means "to the very end, no matter what".
The limiting sense is a disclaimer. It sits with nouns like いけん意見, すいそく推測, めやす目安 and さんこう参考, turns up in business speech and on labels, and often ends in にすぎない or a contrast with が.
With a verb such as しゅちょう主張する, つらぬく貫く or まげない曲げない, あくまでも means the person does not give way, whatever happens.
Before an adjective, the same idea becomes "thoroughly, from start to finish". This sense is mostly written.
あくまでも limits how something should be taken, not how much of it there is. For "only three people" or "only once", use だけ.