You can offset the position of a Source (parent) object in a Multi-referential constraint.

To create offsets in a Multi-referential constraint:

1. Expand the constraints folder in the Scene browser and double-click the Multi-Referential constraint to select it.
2. In the Properties window, expand (Parent object) Offset translation and (Parent object) Offset rotation.
3. Set the Offset translation and rotation for the Parent object you want to affect.
4. Do this for all the parent objects you want to adjust.

You can key and animate this offset by activating the Key and Animate buttons next to each setting you modify.