Here is where I make canonists angry. Boom. So, Sherlock Holmes is kind of like Michael Moorcock’s ‘Eternal Champion.’ Holmes is different than a Paladin of Balance as he isn’t there to restore/maintain balance between Law and Chaos, he’s there to ensure justice in any way it needs to manifest. His mind and prowess are wonders, but his demons stop him from reaching his full potential. As great as he is, as helpful as he is, he cannot ascend past being an excellent consulting detective. He can never ascend to shining hero status. His demons can range from addiction, to misogyny, to broken and unhealthy relationships, or a combination of them all. The constant is that he wages an intense personal/internal battle in every universe. This impedes him from being nothing more than a celestial tool for those seeking redress.

Yes. I said it. The Sherlock Homes story is a multi-versal mythopoesis. We’ll call it the 221B-Verse. Some things are constants (with varying degrees of importance): Holmes, Dr. Watson, Mycroft Holmes, Moriarty, Irene Adler, and Lestrade figures, the 221B Baker Street domicile/headquarters, the Baker Street Irregulars, but each ‘verse has its own specific trappings.
In some ‘verses, Holmes and Dr. Watson are the primary narrative agents. In others, they are more supporting characters a la Enola Holmes and The Irregulars on Netflix (in this ‘verse, the supernatural exists), also see Lovegrove’s “Shadwell and Shadows.”
You have the contemporary 221-B Verses’ like, Sherlock and Elementary and the race and gender-bent Miss Sherlock, and the adjacent-verse of House. We have the original Doyle stories in text, film, and TV — The Adventures of Sherlock Holmes (1984-1994) is stellar. There are the Robert Downey Jr. and Jude Law starring, Guy Ritchie directed films (2009, 2011). The Holmes Cinema-verse also includes Young Sherlock Holmes (1985), The Great Mouse Detective (1986), The Basil Rathbone films (1939-1946, 14 films), and Ian McKellan in Mr. Holmes (2015).

Kareem Abdul-Jabbar’s Mycroft Holmes novels, and all of the stellar research he’s done on the character and the world he inhabits. There are the absolutely wonderful comic book interpretations:

Watson and Holmes by Brandon Perlow, Karl Bollers, and Paul Mendoza, and Baker Street by Gary Reed and Guy Davis. In the digital realm, there is Frogware’s Sherlock Holmes: The Devil’s Daughter and Sherlock Holmes Chapter One video games. And there is the logical union of Lovecraft and Holmes, exemplified by Neil Gaiman’s wonderful short story, “A Study and Emerald” and the other Cthulhu/Lovecraftian Holmes-esque stories, such as Brian Lumley’s “Titus Crow” tales. There is also the fictional meta-commentary on Holmes by the likes of, say, William Hjortsberg’s Nevermore that links Holmes’ creator, Sir Arthur Conan Doyle, Harry Houdini, and the stories of Edgar Alan Poe.
This is by no means an exhaustive list. It is presented to illustrate just how culturally-embedded the Holmes mythology is.

I’d argue that the 221B-Verse isn’t just the films, television shows, and literature that currently exist. The extensive research and commentary that examines it are also a valuable part of the Holmesian rhizome. Sherlock Holmes is one of the most popular pieces of culture in modern history. “A Study in Scarlet” was first published in Beeton’s Christmas Annual in 1887. 134 years later, we’re still fascinated by the arrogant detective and the world he inhabits. What is it about Holmes that continues to intrigue us? Is it his quest to right wrongs? His disciplined mind? Or is it some kind of elusive quality that we cannot decipher, but know that we need? By including the research and commentary that considers Sherlock Holmes, Dr. John Watson, and their (mostly) Victorian and Edwardian settings, the wealth of material produced by the original 56 stories and 4 novels, and all of the contemporary offspring and sibling research, we may be able to solve the central mystery of our flawed Eternal Multi-versal Champion.
I like the idea of a Sherlockian multiverse, but I’d prefer it come up with its own versions and not impinge on all the established alt.Sherlocks (even if it’s implied they’re all out there somewhere).
Thanks for making me aware of Abdul-Jabbar’s Mycroft Holmes books. The library here has them.