Ok, I got the concept down I think. I shall label the two MCs under the names Sun for the guy and Moon for the girl.
Sun is a more upfront type. The idea is to give the idea of a handsome serial killer like character that is capable of interacting with people but hides their darker side very well. Moon is the more obvious but shy type. She creeps people out a little but just how extreme she can be is hidden by her shyness.
The biggest block I had with developing this was coming up with a way to put obstacles in the plot and where it should be leading to, but I think I figured out how to do it thanks to @wings012
and and listening to the song Mira, on repeat for half an hour (This is now the official theme song for this story). Have one of the characters, Sun, be focussed on someone else initially. Setting and age could be either high school or workplace, either works but Moon would be a new addition to the setting, either just transferring or just being hired at the start, for the sake of time, let's just assume this is set in a highschool.
Sun is currently obsessed with someone else but he's a leader of sorts to his classmates thanks to his charisma and takes it upon himself to get Moon settled in. Why would a yandere do this, take time away from the object of their affection? This ties into characterization. The source of Sun's obsessive personality is due to being from an affluent and controlling family. His whole life has been about doing as he's told and giving up on things he likes or wants for the sake of his parents wishes. So his obsessiveness is born out of him going all in on anything he can choose to pursue outside of the control of his family. But he has still been brought up to be proper and a leader and so he does things like this.
On the other side we have Moon, the source of her obsessiveness is born out of a desire to be loved. Her father died early in her life and her mother hates her, seeing her as something that robbed her of her youth and time and that just adds more burdens upon her, she's verbally abusive to Moon. Because of this, Moon lives alone, this is why she's moved to a new school, and is stunted emotionally, shy, has a hard time communicating, and many find her off putting and creepy but she desperately wants someone to love her.
These character backgrounds of Sun and Moon wouldn't be known upfront, they would be revealed in the later half of this story.
So getting back to the setup, that single day of Sun getting Moon comfortable with her new school is enough to set her on becoming obsessed with him. This is when shenanigans can start whether comedic or creepy as we see one yandere go head to head with another as Sun tries to do things to get closer to his current object of affection, let's keep the theme going and call them Star, while Moon tries to disrupt that. This continues for a while until eventually Moon comes to the conclusion that she's no match for Sun and that she's never going to get his affection and so she decides if she can't have that then... She will be happy to at least be his lackey, this is her first sign of character growth, with the lead up initially making you think she's going to kill Sun and/or herself. So she proposes to Sun to be his accomplice in whatever he decides to do and help him with Star, to which he agrees.
More shenanigans, what happens when the full force of two yandere are directed towards one person for the same goal? However, eventually through their plots and schemes, Sun starts to grow fond of Moon, and eventually his affection shifts to her. What is it that leads to this specifically? Moon wanting to be someone in his life despite knowing what the real him is like and also being willing to sacrifice her own wants for him, unlike how his relationship with his parents is where he is the one having to make sacrifices.
So the dynamic shifts again, now we have two yandere that are in love with each other, what hijinks could that cause? Ah, but now we have the genre shift, no longer is this a dark romcom, now this is a romance story tackling emotional problems and unhealthy relationships. One would think that this would be a perfect situation for both of them but now their actual personalities and differences come into play and this is when their backstories would be revealed. Moon is the shy type that doesn't like being the center of attention, suddenly having all of Sun's energy directed at her is overwhelming, the life he lives of being social and seen by others is completely at odds with what she's comfortable with. Further, she's seen the real him and understands his personality better and doubts if this is the actual kind of affection she truly wants or if she's just another obsession for him born from his desire to do what he wants rather than actual love. Sun on the other hand, becomes aware that he's actually causing an amount of pain for Moon and tries to change how he does things and acts to make her more comfortable with him but it lands him into trouble with his parents who don't like these "changes" (Rather, him being more true to himself) nor that he's pursuing someone romantically that isn't carefully selected by them. On the other side of the equation, Moon's mother also becomes aware of this new relationship but unlike Sun's parents, she wants Moon to actively pursue it, demands it even, because Sun is from a wealthy family and Moon getting hitched with him would also give Moon's mom access to that money as "payment" for all the "trouble" she's been. Moon is now even more conflicted over her feelings for Sun since she doesn't want to aid someone that's been so cruel to her but her mother also has a power over her to get Moon to do what she wants
Now we come to the part I'm unsure of, how to conclude this story. I prefer happy endings where things work out but maybe a darker ended mg would be better for this subject matter? I would like a story where Sun and Moon find themselves growing and changing as people thanks to their relationship and finding a way to be happy together. But... We could also go the dark route where, despite their feelings for each other and attempts to be together, the world is hell bent on it not happening and in the end they decide to leave that world by jumping off a bridge together, hand in hand.
There we go, the idea has now taken a full shape.