It appears that, unlike regular 5* heroes, it is currently not possible to continue to level the special skill of a costume past max level for each chevron. If you want to continue to “level up” you must ascend.
For example, my Richard (non-costume) is currently at 3/70 with a maxed special skill at 8. My Richard Costume is also at 3/70, but the special skill is stuck at 6 and I cannot level it any further.
This seems like an issue/oversight to me. Is there some reason why costume special skills cannot be leveled to max without ascending to 4 unlike regular heroes? I want to save my ascension materials for other blues, and I’m perfectly happy to let Richard sit at 3/70. But why can’t I keep feeding him until the special skill is 8 like normal? This is just especially brutal for 5* heroes, because the ascension materials are notoriously scarce, so why not just let us continue to level the special at least?