As far as I know, there's no additional things from a New Game+ aside from Grade Shop, and Elle's affection points. The voiceover is really minor as it only applies to choices.
There's a few quests from the bulletin board that are time limited.
Non-exhaustively,
These aren't particularly well documented. All these quests are red-named, but not all red quests are time limited.
There's a Bad Ending at the end of Chapter 15, if you lose the boss fight there.
There otherwise might be some skits that you could miss if you don't hit select or whatnot.
There's a few quests from the bulletin board that are time limited.
Non-exhaustively,
| JP Name | Translated Name | Chapter Range | Reward |
| 少女のプレゼント | Girl's Present | 1~11? | Elle's Hat |
| 父親のプレゼント | Father's Present | 7~12? | ? |
| エルの忘れ物 | Elle's Lost Item | 6~12? | Item Ball Plus |
| 兄の軌跡・1 | Traces of Brother 1 | 7~12? | - |
| 兄の軌跡・2 | Traces of Brother 2 | 10~12? | - |
| ユリウスとの出会い | Meeting with Julius | 9~14? | Hairpin |
| リドウの依頼 | Redau's Request | 9~14 | Ridau's Sunglasses |
| ビズリーの命令 | Bisley's Orders | 14~15? | Staff ID Card |
These aren't particularly well documented. All these quests are red-named, but not all red quests are time limited.
There's a Bad Ending at the end of Chapter 15, if you lose the boss fight there.
There otherwise might be some skits that you could miss if you don't hit select or whatnot.