because what if Mary was the detective and John was a tech at the forensics lab/morgue and Sherlock was his husband who writes mystery novels and does technical writing for textbooks?
I really like this idea because it isn't John and Sherlock meet and solve crime, it's they've met and fallen in love and one of them helps solve crime and the other solves crime in books and the story is actually about them meeting Mary who does solve crime.
And Mary suffers all the crap a female detective gets saddled with, like all the domestic abuse-related cases because she's more 'sympathetic' and not getting considered for promotion half as much as her male colleagues. She works with Lestrade and Gregson and Hopkins was under her at some point and Irene Adler is trying to get into the detective police force but until then is working drugs and prostitution and education, except it's more drugs and education and not so much prostitution because she thinks all the laws are illogical.
anyway, Mary's usually the one sent to pick up the results from the lab and John's the nice Sikh one who is always ready to explain them to her over lunch, because sometimes she's expected to explain them to everyone else, and one time they schedule lunch and Mary meets Sherlock! who has a total crush on her at first sight, as John explains the next day "He'd looked up all your cases online before dinner and worked backwards to figure out what bits of evidence you discovered and how you did it. He's quite impressed" and Mary's kind of pleased at that but also mortified because she was kind of interested in John, but he's gay and married.
John keeps explaining things over lunch to her though, and Sherlock keeps popping up at these lunches and keeps on interrogating Mary about her cases and how she works things out and pitches stories and cases at her. he get's better and better at interesting ones, not that he was bad in the first place, just formulaic and obvious about the plot and a bit too much of the technical writing leaked into his novel writing.
and then Mary asks why Sherlock got into writing rather than detecting, because he's kind of rubbish at the former but rather good at the latter, and he replies that disseminating knowledge and giving people pleasure is a greater good to the world at large than bringing people to justice.
which then devolves into a threesome proposal because while John is a solid Kinsey six, he is a little smitten with Mary and Sherlock is closer to a four than a five and Mary's kind of fallen in love with him too. (except she doesn't move in, because while Sherlock is a writer and at home most of the time, he's rubbish at housework)
and John's mostly culturally Sikh for obvious reasons, but the entire charity thing is how he met Sherlock in the first place. (he was doing a free lecture somewhere and Sherlock was attending it because information on dead people and they met thus.)