I was messing up with a project lately where I needed dual alphanumerical LCD displays. The plan I had was parallelling them, so I searched the internet about it and couldn’t find anyone that has practically did that, other than that I saw people asking about it at StackExchange.
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.
Here is the result: