A. Basic Control rig hierarchy B. Control rig customized with re-parenting
You can alter how the animation interpolates by changing how effectors react relative to each other. To do this, you can re-parent effectors and change hierarchies in the Control rig.
To provide additional control, you can also create another level of Inverse Kinematics using Auxiliary effectors or pivots. For example, you can make an arm reach further toward an Auxiliary effector without changing the parenting hierarchy.
You can also create other hierarchies in a Control rig by re-parenting certain nodes to added elements. For example, you can add a null element to a Control rig as a parent, and make other effectors the children of the null. By manipulating the null, you can manipulate the hierarchy of bones.