My follower on Twitter began this interesting research.
My initial plan was the following route
Gakken-Nara-Tomigaoka→(Kintetsu Keihanna Line)→Nagata→(Osaka Municipal Subway Chuo Line)→Sakaisuji-Hommachi→(Osaka Municipal Subway Chuo Line)→Tenjinbashisuji-6chome→(Hankyu Senri Line)→Awaji→(Hankyu Kyoto Line)→Juso→(Hankyu Takarazuka Line)→Takarazuka→(Hankyu Imazu Line)→Nishinomiya-Kitaguchi→(Hankyu Kobe Line)→Hankyu-Sannomiya→(Kobe Kosoku Railway Tozai Line)→Kosoku-Kobe→(Kobe Kosoku Railway Tozai Line*1→(Hanshin Main Line)→Amagasaki→(Hanshin Namba Line)→Osaka-Namba→(Kintetsu Nara Line(Formal name is "Kintetsu Namba Line, Osaka Line ,and Nara Line")))→Yamato-Saidaiji→(Kintetsu Kashihara Line)→Yamato-Yagi→(Kintetsu Osaka Line and Nagoya Line)→Kintetsu-Nagoya
But, longer routes can exist.
From Nagata to Tenjinbashisuji-6chome, we can take much longer routes.
I'll show you a longer route.
※The map was cited from PiTaPa.com
I've not yet maken sure that this route on the map is the longest way. Feel free to contact me if you find a longer way than this route.
You had better not take this route really because I don't know whether this route is allowed or not.
*1:Operational name is "Hankyu Kobe Kosoku Line")))→Hanshin-Sannomiya((Formal name is "Sannomiya"