Usually only up to doublechests are intended but with quarks chests and moveable TEs you can make (up to) quintuple chests by pushing them in with a piston:

If you try this with vanilla chests one of them just pops off and drops its content, I think it should work the same way for the quark chests too.
To reproduce just use the setup on the first screenshot, maybe do the same with vanilla chests to see how they behave and try to recreate that for the other chest types.