- do you need the pieces to movement simultaneously:
Here you can see that several can open / close at the same time, each tracking its own movement progress individually. Or one at a time is enough?
- the middle drawer is open
What happens when I click the bottom one? Should the middle one close first?
- can a drawer remain half open?
- can the opening / closing be interrupted?
Trying to establish how feature-rich this needs to be before I suggest something.