How do you parse the noun phrase 'Even the manager herself'?

Question

The Cambridge Grammar of the English Language (Pages 438-9) has these subsections under §13 Peripheral modifiers:

(e) Reflexive pronouns

[7] [The manager h̲e̲r̲s̲e̲l̲f̲] had approved the proposal.

In this construction an NP with the form of a reflexive pronoun functions as post-head modifier within a larger NP; it is an external rather than internal modifier in that the immediate constituents of the matrix NP are the manager + herself (not the + manager herself). [...]

(f) Combinations

An NP may contain more than one peripheral modifier, with multiple layers of embedding:

[8] i Make sure you invite [Jill h̲e̲r̲s̲e̲l̲f̲ t̲o̲o̲].
ii [E̲v̲e̲n̲ m̲e̲r̲e̲l̲y̲ a formal apology] would be acceptable.
iii After [f̲i̲n̲a̲n̲c̲i̲a̲l̲l̲y̲ c̲e̲r̲t̲a̲i̲n̲l̲y̲ the worst crisis this decade], the emerging economies will take some time to recover.

The bracketed NP in [i] has the NP Jill herself as head and the adverb too as peripheral modifier; at the next level, the NP Jill is head and the NP herself is peripheral modifier. A peripheral modifier is thus in peripheral position (initial or final) in the NP of which it is an immediate constituent, but need not be in peripheral position in a larger NP containing it.

Based on this, I wonder how we should parse the noun phrase 'Even the manager herself' as in [7']:

[7'] [E̲v̲e̲n̲ the manager h̲e̲r̲s̲e̲l̲f̲] had approved the proposal.

Here, both Even and herself are what CGEL calls peripheral modifiers. Here are some parsing options I can think of:
(1) E̲v̲e̲n̲ + [the manager + h̲e̲r̲s̲e̲l̲f̲];
(2) [E̲v̲e̲n̲ + the manager] + h̲e̲r̲s̲e̲l̲f̲; or
(3) E̲v̲e̲n̲ + [the manager] + h̲e̲r̲s̲e̲l̲f̲

Which is correct? Or is there any other way?

Answer 1

The three possibilities being considered are:

1. [Even [[the manager] herself]] had approved the proposal.
2. [[Even [the manager]] herself] had approved the proposal.
3. [[Even] [the manager] [herself]] had approved the proposal.

First, consider that we can replace the NP "the manager" with an NP-coordination:

4. Even the manager and the client themselves had approved the proposal.

We can do the same with "the manager herself":

5. Even the manager herself and the client himself had approved the proposal.

But we can't do this with "even the manager":

6. * Even the manager and even the client themselves had approved the proposal.

Coordination is not necessarily a perfect guide to syntactic structure, but, all else being equal, if a sequence of words can be coordinated, we should treat it as a syntactic constituent; certainly none of the kinds of non-basic coordination H&P list apply here (see pp. 1348-1350). So it seems that we should take "the manager herself" to be a constituent, but not "even the manager."

So this counts strongly in favor of analysis (1), "[Even [[the manager] herself]] had approved the proposal."

Answer 2

Herself is a pronoun and stands in apposition.

OED: Herself (pron.):

I.1. In apposition to a personal noun (as subject or object) or to a subjective pronoun: that particular female person or animal, etc.; the female person in question personally.

In early use also in apposition to grammatically feminine nouns. Occasionally used in relation to a singular noun or pronoun of undetermined gender.

OE Ðeos eorðe is geworht, ac heo nis na hyre sylf lif. [My translation: This earth is created, but she is not herself life] Ælfric, Homily (Vitellius MS. C.v) in J. C. Pope, Homilies of Ælfric (1967) vol. I. 208

1945 She herself was probably more than a little frightened of her own sexuality. N. Streatfeild, Saplings xiv. 224

Even is an adverb - often an emphatic free modifier:

Even (adv.) II.8.a. Used to convey that what is being referred to is an extreme case in comparison with a weaker or more general one which is stated or implied in the adjacent context. Prefixed to the particular word, phrase, or clause in which the extremeness of the case is expressed.

2007 Even the newest New Yorker knows that the furthest eastern border of Greenwich Village is Fourth Avenue. Time Out New York 18 January 24/3