I like this question because it's challenging. Oxford Dictionary of English gives the example
She is more than happy to oblige.
For this structure (i.e. 'more than' + adjective), the dictionary places 'more than' in the adverb category and defines it as
extremely (used before an adjective conveying a positive feeling or attitude)
Now, my best surmise is that in your example 'more than' acts as an adverb too, and could be replaced with a word like 'utterly' without any significant change in meaning:
You'd think that would be utterly enough for most of us but meanings change and new words are being created all the time.
If so, 'enough' is the head of an adjective phrase, which functions as the complement.
1Why do you need to know which is the head word? Which do you think it is, and why? It's easier for people to help you if we have as much information as possible. – SamBC – 2019-02-23T13:42:46.233
@SamBC It's because I'd like to know (curiosity is the king). I think two ways are probable. The first way is: that would be 'more' than enough. In this perspective, 'more' is the real complement (the head of the complement), 'than enough' being the complement of the 'more'. The second way is: that would be more than 'enough'. In this aspect, 'enough' is the real complement, 'more than' itself as a set being the intensifier/premodifier of the 'enough'. – JYJ – 2019-02-23T16:29:22.397
1The fused determiner-head "enough" is the head. "More than enough" is a noun phrase functioning as complement of "be", in which "more" is a determinative phrase. "Enough", which functions as complement of "than" is called a 'fused' head because it is at the same time a determiner and also the head, cf. "enough words". – BillJ – 2019-02-23T18:17:40.603
@BillJ Thanks a million. Thanks to you, I understand 'enough' is what. Might I enquire of you a supplementary question about 'more than'? Did you mean that 'more than' is a determinative phrase and 'more' is the head of the determinative phrase, 'than' being the complement of 'more'. (with 'enough' as complement of 'than') – JYJ – 2019-02-23T23:30:46.150