Many shape-changing interfaces use an array of actuated rods to create a display surface; each rod working as a pixel. However, this approach only supports pixel height manipulation and cannot produce more radical shape changes of each pixel (and thus of the display). Examples of such changes include non-horizontal pixels, pixels that overhang other pixels, or variable gaps between pixels. We present a concept for composing shape-changing interfaces by vertically stacking tilt-enabled modules. Together, stacking and tilting allow us to create a more diverse range of display surfaces than using arrays. We demonstrate this concept through TiltStacks, a shape-changing prototype built using stacked linear actuators and displays. Each tiltable module provides three degrees of freedom (z-movement, roll, and pitch); two more degrees of freedom are added through stacking modules (i.e., planar x- and y-movement).