There are 20 x 6 line LCD displays out there BUT trying to get them to work with an Arduino is a real 'bang your head on the wall' experience.
The Batron BT62005P (aka Batron 2006A-P1) is exactly that beast.
I acquired several as a gift some time back and I think that was because the previous owner had given up on them.
I spent a lot of time experimenting with them trying them as multiple HD44780 devices as well as KS0073 devices as the minimal data sheet claims that's their base chip.
I also found people quoting that the display could use a SPLC780 device but could not confirm it.
The Batron has twin enable lines but they seem to have very odd functions during use.
I chose to carry on my research off of the forum due to the very much holier-than-thou attitude of some respondents to my questions. They seem to have forgotten that they were beginners once and now, having learnt to walk on water and fly without wings needed to preach from their lofty towers.
If you need more lines I'd suggest simply stacking a pair of HD44780 based 20x4 displays and either using them as separate instances of LCD or using I2C and having them on different addresses. Both situations work and work well, I2C being the better bet as it frees up your lines for other things.
Dale H