There are 176 hits in COCA for [be] so much a part of, including the title and:
1- It actually is so much a part of life.
2- Law is so much a part of me, I don't think I'll ever be able to let loose of it.
3- The computer is so much a part of her sons' lives that they sometimes bring a laptop when they visit family in the East Bay.
Other similar examples from COCA:
4- it is so much a pleasure to have you here.
5- And your film is so much a woman's story, a young woman story.
6- I am so much my mother's child in that respect. I hear myself channeling her in so many ways.
Other examples from COCA featuring so alone:
7- I go to farmers' markets all the time. Field-to-table is so my thing.
8- Oh, yeah! This is so my type of wish!
9- "That is so fucking bizarre," she says. "But it 's so your mom."
10- Dude, try it. This is so the bomb.
11- If you want to hire me, this is so the wrong way to go about it.
12- even though she's dead tired and she's been up all night in labor, the minute her baby calls, she is so there.
13- He was so here, he pressed with impossible mass against the Earth.
[Be] so much a part of seems to be a special case, or even an idiom†, but I have more general questions:
1- What does so much modify in the sentences above? The verb be?‡
2- If yes, can be be freely modified by so much? If not, when exactly can be be modified by so much?
3- Why doesn't so alone work in [be] so a part of? (There are 2 hits for it in COCA (compare with the 176 mentioned above)) In other words, when exactly can be be modified by so alone?§
Note: In all the examples above, the predicative complements are noun phrases. I think things get more familiar and a lot easier to explain (for me at least) when the complement after so or so much is an adjective or something (but this post is not about that):
-Hi! You're so hot!
+Thanks! You're so much hotter than me!
-I'm so(/so much) in love with you!
+Wow! I'm so married to you!
† You can see that the title and #3 have that after so much, #2 suggests that that, and #1 doesn't have the that. I'm not sure how big of a difference it makes in the meaning, or how relevant it is to my general concerns here.
‡ Note that the verb be is modifiable.
§ One casual theory states that when the situation is gradable (or perceived as such) so much works better, and when it's non-gradable so may be fitter. Compare #2 to #10 for example. (or any of #1-#6 to any of #7-#13)