Not my work but thought this is interesting:
this book
shows a "double direction" interaction between maxilla and the pituitary gland:
"The work recently done in this field by Dr. Hector Mortimer and his associates in McGill
University, Montreal, has included studies of skull development of rats. He has shown that the
surgical removal of the pituitary body at the base of the brain in very young rats produces regularly a certain type of defect in skull development. This has been characterized by a lack of development forward of the muzzle or face, with a narrowing of the nose and dental arches. He found that by the addition of extracts made from the pituitary glands, which he had removed surgically, he entirely prevented the development of these defects, thereby establishing the relation of the injury to deficiencies of the hormones developed by that organ."
It is the first "direction" of the relation, it could mean that aside mechanical pressure posture, etc, chemicals will affect the palate's width.
He also talks about the lack of vitamin E:
"The changes observed [by vitamin E deficiency] are similar in several ways to those produced by hypophysectomy (removal of pituitary gland). Marked degranulation of the anterior pituitary is found in both the abnormal young and the adult sterile animals. Lack of vitamin E therefore produces a virtual nutritional hypophysectomy in the young rat."
Well, it shows the importance of vitamin E for good pituitary and therefor good hormonal balance. If we link it to Ray Peat's work on PUFAs (polyunsaturated fatty acids), we can guess that excess PUFAs negatively affect the pituitary and therefore the maxilla and palate. I'm only making the link with what I know, we don't know how much, etc.
And more importantly, the other relation from maxilla to pituitary:
"A striking case is that of a boy sixteen years of age who was a typical Mongolian idiot. [...]
This boy at the age of sixteen was infantile in many of his
characteristics and developments. The genitals were those of a boy eight years old. The facial expression was that of the typical Mongolian idiot. By the Binet test he had a mentality of about four years. Roentgenograms of his hands showed that the epiphyseal bones had not united. [...]
The outstanding physical characteristic was his maxillary arch which was so much smaller than the mandibular arch that it went entirely inside it. In order to give him a masticating surface, and with the hope of helping him both physically and mentally, since several cases had greatly benefited by such an operation, I determined to widen his arch by moving the maxillary bones apart about one-half inch. "
This is the before/after 30 days / after 6 months pics
And what is shocking is the pic's legend:
"Aged sixteen,
infantile before, adolescent after operation. While he
improved mentally he was harmless before and a sex pervert
after operation and had to be placed in an institution."
And then:
"With the movement of the maxillary bones laterally, as shown progressively in Fig. 126, there was a very great change in his physical development and mentality. He grew three inches in about four months. His moustache started to grow immediately; and in twelve weeks' time the genitals developed from those of a child to those of a man, and with it a sense of modesty. His mental change was even more marked. The space between the maxillary bones was widened about one-half inch in about thirty days. This lateral pressure on the maxillary bones was accomplished by rigid attachments to the teeth of the two sides of the upper arch. The outward movement of the maxillary bones (which form the roof of the mouth and sides of the nose) by pressure on the temporal bones produced a tension downward on the floor of the anterior part of the brain, thus stimulating the pituitary gland in the base of the brain. In a few weeks' time he passed through stages that usually take several years."
this book
shows a "double direction" interaction between maxilla and the pituitary gland:
"The work recently done in this field by Dr. Hector Mortimer and his associates in McGill
University, Montreal, has included studies of skull development of rats. He has shown that the
surgical removal of the pituitary body at the base of the brain in very young rats produces regularly a certain type of defect in skull development. This has been characterized by a lack of development forward of the muzzle or face, with a narrowing of the nose and dental arches. He found that by the addition of extracts made from the pituitary glands, which he had removed surgically, he entirely prevented the development of these defects, thereby establishing the relation of the injury to deficiencies of the hormones developed by that organ."
It is the first "direction" of the relation, it could mean that aside mechanical pressure posture, etc, chemicals will affect the palate's width.
He also talks about the lack of vitamin E:
"The changes observed [by vitamin E deficiency] are similar in several ways to those produced by hypophysectomy (removal of pituitary gland). Marked degranulation of the anterior pituitary is found in both the abnormal young and the adult sterile animals. Lack of vitamin E therefore produces a virtual nutritional hypophysectomy in the young rat."
Well, it shows the importance of vitamin E for good pituitary and therefor good hormonal balance. If we link it to Ray Peat's work on PUFAs (polyunsaturated fatty acids), we can guess that excess PUFAs negatively affect the pituitary and therefore the maxilla and palate. I'm only making the link with what I know, we don't know how much, etc.
And more importantly, the other relation from maxilla to pituitary:
"A striking case is that of a boy sixteen years of age who was a typical Mongolian idiot. [...]
This boy at the age of sixteen was infantile in many of his
characteristics and developments. The genitals were those of a boy eight years old. The facial expression was that of the typical Mongolian idiot. By the Binet test he had a mentality of about four years. Roentgenograms of his hands showed that the epiphyseal bones had not united. [...]
The outstanding physical characteristic was his maxillary arch which was so much smaller than the mandibular arch that it went entirely inside it. In order to give him a masticating surface, and with the hope of helping him both physically and mentally, since several cases had greatly benefited by such an operation, I determined to widen his arch by moving the maxillary bones apart about one-half inch. "
This is the before/after 30 days / after 6 months pics
And what is shocking is the pic's legend:
"Aged sixteen,
infantile before, adolescent after operation. While he
improved mentally he was harmless before and a sex pervert
after operation and had to be placed in an institution."
And then:
"With the movement of the maxillary bones laterally, as shown progressively in Fig. 126, there was a very great change in his physical development and mentality. He grew three inches in about four months. His moustache started to grow immediately; and in twelve weeks' time the genitals developed from those of a child to those of a man, and with it a sense of modesty. His mental change was even more marked. The space between the maxillary bones was widened about one-half inch in about thirty days. This lateral pressure on the maxillary bones was accomplished by rigid attachments to the teeth of the two sides of the upper arch. The outward movement of the maxillary bones (which form the roof of the mouth and sides of the nose) by pressure on the temporal bones produced a tension downward on the floor of the anterior part of the brain, thus stimulating the pituitary gland in the base of the brain. In a few weeks' time he passed through stages that usually take several years."
Dont wanna fall in the "muh detox" movement 
