Two common techniques that do not appear to have been mentioned previously are:
(1) Traditional 'Serial' using Tx (and possibly Rx)
(2) Shift register
Obfuscate: To make so confused or opaque as to be difficult to perceive or understand.
Also: In case you don't already know this, any technique used to control a 16x2 device will also work with a 16x4 with no extra wires.
Don