I had a new theory after rereading the manga. Noting that after Suguro did some digging around with the Section 13, he found the Shiro was a clone, 004, but it skips to 006, meaning 005 if missing. Shiemi has a secret that she isn't letting up on, not even we readers know what it is, so it's just a thought, but what is she's the missing clone?
Unlikely. 005's name has been shown to be Goro in the files, and since Azazel posseses a human male, all of his clones are male. He's also suspected to be the clone Satan possesed, and we saw him (I think it was him) in a gootank a while back.
Basically, if Shiemi is a clone, she'd have to be the clone of a demon "queen", and the only 3 who were cloned were Lucifer, Samael and Azazel, all males, so she most likely doesn't come from that section of the experiments.
On another note, since I was thinking about biology, I came up with the -stupid and weird- idea that the Moriyama family doesn't need men to reproduce. Women are XX and men are XY, so assuming they aren't artificial clones... could they just use a similar process to scissiparity? Like you make a clone baby in your womb?
I was thinking something vaguely similar to all of this.
This is the rough theory I'm using with my fic, by the way, so I'm sorry for the spoilers for
Coming into Bloom that I'm throwing out in the open. I know at least a couple of you are reading it.

I've already started touching on it, and I've said a lot of this on tumblr, so it shouldn't come as a surprise. Sorry, I'm really not trying to plug it.
And here we go...
What if Shiemi's grandmother was actively involved with section 13, not just in sanctioning it as a Girgori (potentially), but using what Nephilim abilities she had (powers of creation and life) to help begin the cloning process. As time went on and things got more successful, perhaps she herself started either donating samples for her own cloning or reproduced with a genetically enhanced Lucifer clone [given Shiemi's coloring] to revive the Shemihaza Nephilim line's potential, meaning she would have had two daughters: the one who runs the shop and another.
The resulting daughter, Maria, (not the one we see at the shop), when she was old enough, was either mated to another enhanced Lucifer or Azazel clone in section 13 or after things split off into the Illuminati, OR gave birth to a further enhanced clone of herself.
THAT daughter [Shiemi, a second generation clone or naturally produced daughter of enhanced clones] was kidnapped or given to the grandmother for safe-keeping and to be raised in a garden with little contact with the outside world in order to attune her with nature and keep her personality at a minimum. I was thinking to either be a
temporary host to Shemihaza (for a final battle situation) or be pushed into the state that Nephilim originally were: immensely powerful, potentially rivaling the powers of the mid/upper level Demon Kings.

I think Shiemi would become enhanced should she reach the Garden of Amahara, which I theorize is Shemihaza's domain. Both her "mother" (one who runs the shop) and grandmother have both tried to find it, and presumably failed, however the grandmother thinks Shiemi will reach it one day. I don't think it's a fairytale situation.
In any event, I feel her grandmother isn't the nice lady she pretended to be, at least not to the extent Shiemi believes. Besides, why would she live in a shed when a perfectly comfortable, sizable house was meters away. She was hiding crap, even if it's not like the secret underground garden in the anime.
As an aside: Another thing that makes me kinda think this is that Maria Yoshida from the Illuminati looks REMARKABLY like Shiemi, and would have wanted to save Izumo, who was the age her own daughter [Shiemi] would be, and her younger sister. Maternal grief at not having her own daughter in her life and the thought of her own daughter being subjected to experimentation would possibly make her want to sacrifice her safety and assist in Izumo and her sister's escape.
It would also explain the "mother" at the shops apathy for Shiemi: Shiemi is not her daughter (actually her niece, which would explain why they still look similar enough to be related) and Shiemi is a "chosen one," being cultivated and groomed by both her mother (the grandmother) and Mephisto. She ["mother'] may be a Nephilim as well, but she's not special like Shiemi, which would potentially make her turn to the Illuminati and possibly be involved in the elixirs and demon eating, herself. I think she wants power, much like Yukio's jealousy of Rin, and Saburota Toudou. She might have hated Maria and her mother, as well.
I also think she's the current Shemihaza Girgori, as well as the spy the Order is looking for, 100%. But that theory has already been covered several times.

The image should cover all generations and Shiemihaza theory things in a simplified, if not already assumed manner. All of their hair is light colored with bangs swooping to the left side of the face. Shiemi's hairstyle is far more in line with Maria's (practically a carbon copy at this point) than her "mother's" and grandmother's, and while that can be an easy fix by pulling it up and rolling a solitary trailing curl, it's drawn that way on purpose. All of them having similar face and eye-shapes.
It's hardly a coincidence for Maria Yoshida to look the way she does.
So far, every family we've been introduced to looks like they are truly genetically related. The Shima clan's sleepy eyes and unruly, spiky hair, the Todou family's eyes and hair, the Okumura twin's eyes and hair (though they have the most differences out of all of these examples, esp post 98). Bon distinctly looks like a blend of his mother and father... these are not generic manga faces Kato draws.
I really hope I made sense with that. I can't find more eloquently written story notes, atm.
EDIT:
And ACTUALLY, come to think of it, Shiemi's "mother" (one at the shop) looks significantly older than Maria, soooo, if Maria is related, it COULD go more like this:

In THAT case, she'd be a 3rd generation enhanced clone by-product and pedigreed, whether males were used or not.
In THAT case, she'd be a 3rd generation enhanced clone by-product and pedigreed, whether males were used or not.
If the alternate is the case, the “mother’s” apathy could also be that she already lost her REAL daughter [Maria] first to the Illuminati and then death, and she’s distancing herself emotionally from her granddaughter [Shiemi] because she knows what her mother and Mephisto were/are planning for her, to some degree. The Illuminati ties could still be plausible in this case, but more in the vein of having a vendetta against her own mother and Mephisto for the inhumane treatment of their family (genetically designed and groomed for the sole intent to use as a tool), despite the Illuminati being just as guilty AND being the ones that killed Maria. Or, it could apply that she is a jealous, untalented Nephilim, and wants power, as in the first scenario as well.
Or a third possibility:
Just posted this on Blue Knight, but figured I’d do it here, too, since not everyone goes there. It ties in with some other things I’ve posted as theories, so forgive anything that feels repetitive from my previous ones.
And here we go...
What if Shiemi's grandmother was actively involved with section 13, not just in sanctioning it as a Girgori (potentially), but using what Nephilim abilities she had (powers of creation and life) to help begin the cloning process. As time went on and things got more successful, perhaps she herself started either donating samples for her own cloning or reproduced with a genetically enhanced Lucifer clone [given Shiemi's coloring] to revive the Shemihaza Nephilim line's potential, meaning she would have had two daughters: the one who runs the shop and another.
The resulting daughter, Maria, (not the one we see at the shop), when she was old enough, was either mated to another enhanced Lucifer or Azazel clone in section 13 or after things split off into the Illuminati, OR gave birth to a further enhanced clone of herself.
THAT daughter [Shiemi, a second generation clone or naturally produced daughter of enhanced clones] was kidnapped or given to the grandmother for safe-keeping and to be raised in a garden with little contact with the outside world in order to attune her with nature and keep her personality at a minimum. I was thinking to either be a temporary host to Shemihaza (for a final battle situation) or be pushed into the state that Nephilim originally were: immensely powerful, potentially rivaling the powers of the mid/upper level Demon Kings.
I think Shiemi would become “ascended” or “further empowered” should she reach the Garden of Amahara, which I theorize is Shemihaza's domain. Both her "mother" (one who runs the shop) and grandmother have both tried to find it, and presumably failed, however the grandmother thinks Shiemi will reach it one day. I don't think it's a fairytale situation.
In any event, I feel her grandmother isn't the nice lady she pretended to be, at least not to the extent Shiemi believes. Besides, why would she live in a shed when a perfectly comfortable, sizable house was meters away. She was hiding crap, even if it's not like the secret underground garden in the anime.
As an aside: Another thing that makes me kinda think this is that Maria Yoshida from the Illuminati looks REMARKABLY like Shiemi, and would have wanted to save Izumo, who was the age her own daughter [Shiemi] would be, and her younger sister. Maternal grief at not having her own daughter in her life and the thought of her own daughter being subjected to experimentation would possibly make her want to sacrifice her safety and assist in Izumo and her sister's escape.
It would also explain the "mother" at the shops apathy for Shiemi: Shiemi is not her daughter (actually her niece, and why they still look similar enough to be related) and Shiemi is a "chosen one," being cultivated and groomed by both her mother [the grandmother] and Mephisto. She ["mother'] may be a Nephilim as well, but she's not special like Shiemi, which would potentially make her turn to the Illuminati and possibly be involved in the elixirs and demon eating, herself. I think she wants power, much like Yukio's jealousy of Rin, and Saburota Toudou. She might have hated Maria and her mother, as well, for not thinking she was enough and saddling her with the shop.
I also think she's the current Shemihaza Girgori, as well as the spy the Order is looking for, 100%. But that theory has already been covered several times.
The image should cover all generations and Shiemihaza theory things in a simplified, if not already assumed manner. All of their hair is light colored with bangs swooping to the left side of the face. Shiemi's hairstyle is far more in line with Maria's (practically a carbon copy at this point) than her "mother's" and grandmother's, and while that can be an easy fix by pulling it up and rolling a solitary trailing curl, it's drawn that way on purpose. All of them having similar face and eye-shapes.
It's hardly a coincidence for Maria Yoshida to look the way she does.
So far, every family we've been introduced to looks like they are truly genetically related. The Shima clan's sleepy eyes and unruly, spiky hair, the Todou family's eyes and hair, the Okumura twin's eyes and hair (though they have the most differences out of all of these examples, esp post 98). Bon distinctly looks like a blend of his mother and father... these are not generic manga faces Kato draws
I ascribe to the above, but it could also go as follow....
An alternative family tree to the above:Shiemi's "mother" (one at the shop) looks significantly older than Maria, soooo, if Maria is related, it COULD go more like this:

In THAT case, she'd be a 3rd generation enhanced clone by-product and pedigreed, whether males were used or not.
If the alternate is the case, the “mother’s” apathy could also be that she already lost her REAL daughter [Maria] first to the Illuminati and then death, and she’s distancing herself emotionally from her granddaughter [Shiemi] because she knows what her mother and Mephisto were/are planning for her, to some degree. The Illuminati ties could still be plausible in this case, but more in the vein of having a vendetta against her own mother and Mephisto for the inhumane treatment of their family (genetically designed and groomed for the sole intent to use as a tool), despite the Illuminati being just as guilty AND being the ones that killed Maria. Or, it could apply that she is a jealous, untalented Nephilim, and wants power, as in the first scenario as well.
Or a third possibility:
In which Maria and Shiemi are clones and sisters, born many years apart, and Maria was a failed experiment (no/lackluster abilities).
OR, like more in the vein of what @Khalumia said, but COMPLETELY artificially created ... and I won’t make a graphic for this one: Shiemi, Maria, and Shiemi’s “mother” are all sisters born from the grandmother being enhanced and cloned (even if she didn’t give birth to them herself) many, many years apart, a new one being born after they failed to “ascend” or weren’t powerful enough, with a lot of genetic tweaking done in between. So much trial and error. Wait 15 years only to find the kid you’ve created is a “dud”, tweak, then try again.