LCDs larger than 20x04 and 5" diagonal
Naked displays... search e.g. Ebay for "40x4 lcd" (maybe enable "worldwide" search)...

...naked... so not i2c ... but Arduino libs for these displays exist (e.g.: liquidcrystal440), so add an Arduino-Pro or such and you can have i2c... basically they are two 40x2 displays on the same spi bus selected by different chip select lines...