Japanese Dramas about friendgroups/found family, character development

Maybe try Holyland (2005)  

It's pretty much got everything you want, except the cast is quite small in numbers :)

Attention Please - friendship among cabin attendants, comedy
Beginners! - like police academy
Blue Birthday - school thriller, romance, fantasy
Cheer☆Dan - all girls sports comedy
Good Luck!! - friendship in aviation industry, romance
Hammer Session! - school comedy with a class of misfits, similar to GTO
Hatsumori Bemars - all girls sports comedy
Hello Harinezumi - mix of many things, detective comedy, but fbromance of main detctives is outstanding.
Joshi Kousei no Mudazukai - daily lives of some weirdos in high school and their teacher
Kokoro no Fufufu - some fantasy school
Limit - school thriller, psychological, action and friendship too. They need to work together to survive.
Tori Girl - a movie, but great and about school friendship
Tsuiraku JK to Haijin Kyoshi - school comedy/ with outstanding chemistry between a teacher and his female student.
Yamada-kun to 7-nin no Majo - school comedy, romance, magic
Yuru Camp△ - school, friendship, female centered

Some cast is bigger, some smaller. Hopefully you find something good among these recs. :)

• Kieta Hatsukoi has a cute friendship between one of the MLs, the SML, and the FL (it's a High School BL and the secondary couple is the SML/FL).
• Hana Yori Dango (high school, the four guys are friends)
• Kimi no Hana ni Naru (the band are friends)
• Maiko-san Chi no Makanai-san (female friendship, no romance)
• One Piece (kind of found family/unlikely friends)

Hayako Sensei is about a friend group of elementary school teachers at a small school. They have always had personal projects together, like fitness. Then they decide to find spouses as a group project. The FL is in her early 30's and feel she ought to be interested in marriage, but she has been satisfied living with her parents. Very likeable people in this one.

A Drama that might fit many of your requirements is Quartet (2017) - 4 misfits who come together to form a string quartet, and live in the same house. They effectively become a family by the end.  There's no real romance though