Hopefully. I like to speculate that there will be a final fourth Route. Our Black Wolf Friend has often teased Luke that he cannot save everyone and there is simple not enough time. So maybe Luke will be forced to decide between saving Cooper or Max on Max Route, one of them will be killed. (Rausmutt wanted to switch up a few thing after all). Saveing Cooper gives Luke valubale insight in Authority among the good boys, maybe allowing him to finally rally the frightful Shiba and Great Dane.
In the end Luke need to save Cooper and Max at least once and play all the good endings of the other Route to unlock the Final Route that is focused on all characters at once including Cooper AND Teak !!
So the Final Route with Teak can play out like this:
After the Intro Luke listens to Teak and Max to hear about Cooper Injury. then Luke will join Burry to cook a meal for cooper alone. [ Time spend with Burry; CHECK!] . Once afternoon arrives, Luke goes to Cooper first. This time around Cooper wins over his "anxiety towards Luke" and we got a nice Chat between Cooper, Twistle and Luke about what happened, twistle new Rifle and Teaks past maybe. [Time spend with Cooper and Twistle: CHECK!] Teak also joins instead of casuing a fit. After that Teak and Luke both join Runes Training; [Time spend with Rune and his class: CHECK!] from now on Luke and Teak will stay together for most of the day. This time the siuation between Teak and Luke get resolved, thanks to Coopers stories about teak past. After Rune and Luke got the closing chat, Luke and Teak leave to met Max, spending time with him and Dandelion. [Time spend with Max and Dandelion: CHECK!] Maybe Teak and cooper will then join the Bath with the others.
Thats my prediction. Take care.