'even': How might've the sense of 'introducing an extreme case of something more generally implied' arisen from 'emphasizing identity'?

I quote only the germane sentences from Etymonline on 'even (adj.)':

The adverb is Old English efne "exactly, just, likewise."
Modern adverbial sense
([2.] introducing an extreme case of something more generally implied [End of 2.])
seems to have arisen 16c. from
[1.] use of the word to emphasize identity ("Who, me?" "Even you") [End of 1.].
Etymologists are uncertain whether the original sense was "level" or "alike."  

3. Please see this question's title.

4. What semantic notions underlie 1 and 2?

Solution 1:

Here's my theory of how it could have happened.

The phrase "even X" in sense [2] is often used in cases where X seems to be (or assumes himself to be, when X is a person) an outlier -- if they were normal, it wouldn't be necessary to emphasize the specific case.

Since they're an outlier, they're considered an extreme case of whatever quality distinguishes them from the general case. And this is how "even" became used to indicate extreme cases in general.