You might argue Chinese has four as well: trad. hanzi, simplified hanzi, pinyin (which is learned before hanzi), and zhuyin, though of course any one country only uses two of those.
Don't forget seal script, grass script etc.
Dozens of languages in Central Asia have been written with three or more scripts. Those that used Arabic or Mongolian and came under Soviet control switched to Roman and then to Cyrillic. Uyghur was written in Sogdian, the the Uyghur script (unless you want to count that as just a latter local form of Sogdian), occasionally Orkhon (Turkic "runes"), occasionally Syriac, then Arabic, Roman, and Cyrillic (local forms). That's what, seven?
I think Mongolian has had upwards of seven as well. Mongolian, Clear Script, Soyombo, Latin, Cyrillic, Chinese, Arabic etc.
Kurdish has been written in Arabic, Sorani, Armenian, Roman, Cyrillic. (Sorani looks like Arabic, but is functionally a full alphabet.)
Technically it's an extended Arabic alphabet, but I'll let this one slide.
Serbocroatian has been written in Croatian Cyrillic, Serbian Cyrillic, Glagolitic, Arabic, and the now-dominant Gaj's Latin.
There's a Croatian and Serbian Cyrillic? How much can they possibly differ?