I have this theory about Sherlock Series 4, and I wanted to share it before the new episode before the new episode comes out so I can give myself credit if I'm right. :)
I think it's possible that Sherlock has multiple personalities, and the third Holmes brother, Sherrinford, is one of his personalities. Sherlock's parents don't have any pictures of Sherrinford, and they are the type of people who would have photographs of a child who died or left the family. The parents must not know about this supposed "third brother".
It was also said in a preview for series 4 that Sherlock's "darkest secret" would be revealed. This could be referring to the fact he has multiple personalities.
Mycroft also says "Redbeard" when Sherlock seems to be going off the edge, and Redbeard may be a trigger word that brings Sherlock back to himself when he is slipping into Sherrinford. In s4:e1 Sherlock also told Mrs. Hudson to say a code word if she feels as though he is slipping off the edge.
Sherrinford may have been a brother at one point, but perhaps he was still born. My theory is that Sherlock wanted a little brother so badly that this brother, who never existed in the first place, that Sherrinford became his imaginary friend. This would explain why there are no pictures of Sherrinford in Sherlock's parents' house. Sherrinford never existed.
Perhaps Sherlock suffered an extremely painful loss of some other event that caused him to have a psychotic break. His imaginary friend developed into its own person, residing in Sherlock's brain.
Just a theory, so don't judge or hate on me if I'm wrong! Thanks for reading!!!