Abdullah explored the idea of driving two character LCDs in parallel. When he couldn’t find any information about this online, he decided to try it out himself.
Then I thought about it and I gave it a go. The result is positive! However, there is a gotcha; if you are using LCDs from different manufacturers or different types, the contrast setting might differ, as it did in my example. In order to overcome this, I would suggest putting two potentiometers in your board to adjust the contrasts individually. And don’t forget, you are using one more LCD, meaning more back light current. If you are using a 7805 without a heat-sink, you should re-calculate your thermal values.