Complex collision for moving objects

Does UE4 support moving objects with complex (per-poly) collision? I tried setting the chair from the default scene to “use complex collision as simple” (basically, collide per-poly), and no matter what settings I mess with I can’t get it to collide with the floor, and it falls right through.

The settings I currently have are:

chair - set to per-poly collision, collision enabled, object type set to physics body, set to block everything, use CCD checked, trace complex on move checked

floor - uses 6-DOP (box) collision, collision preset is BlockAll.

As far as I know there is no complex collision for moving objects. Neither for meshes used on spline actors. You need a traditional collision model.