A Different Trio
On what was supposed to be Hikigaya's first day of high school, he was struck by a car in an attempt to save a dog that had broken of its leash and was going to be hit by the car. The injury keeps him out of school for a sizeable amount of time that by the time he's back all the friend groups have been made and Hikigaya is alone once again.
However in this case he is able to make some friends, two in fact in the form of Kawasaki Saki and Totsuka Saika who sit close to him in class.
These two are the only named Oregairu characters in the class apart from Hiratsuka Sensei.
They get to know each other as Totsuka being the nice guy he is wants to get to know his new seat mate and is curious about why he wasn't in school from the start. Kawasaki actually saw what happened that day from a distance and got curious about things after Hikigaya mentioned he was the one involved in the incident. Kawasaki is able to get closer over similarities she, Hachiman and Totsuka have.
The 3 get closer with each other and spend more time with each other, eating lunch together and such, even spending time together outside of school.
Could have Kawasaki's whole working late situation be fixed a lot earlier with Hikigaya and Totsuka's help.
Due to making friends at this stage, Hikigaya doesn't develop quite the cynical attitude and mindset that he had at the start of the series, thus not requiring him to be forced into the service club in his second year.
Could possibly have Hikigaya join the tennis club with Totsuka.
Also can combine this with the 'Student Council' idea and have Hikigaya apply for a place in the Student Council in first year after Shiromeguri Meguri is elected. Meguri can either become a sort of big sister figure for Hikigaya or possibly something romantic
The trio live a very drama free and enjoyable time together. If you want Hikigaya to get into a relationship then Saki is the pick.
