Generate custom sprite characters

I'm trying to make a 2D game where you can choose different parts for your character appearance: his eyes, his hair, his body... Every part has a little animation (for example, the eyes can open and close), and all animations are made with classic pixelated sprites.

So, basically, what I'd like to do is to generate a character attaching different body parts. Of course, I'm not asking you to explain me the whole process -that's for me to research-, but I'd like to know if it is possible, and if it's relatively fast to do, and the main points on how should I do it. Any advice will be appreciated!

Thanks for your attention!