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The Design of Experiments (DOE) works through parametric updates, which are just changes in dimensions. If you are making topological changes there should be many other problems that will prevent it from working. With parametric updates, IDs don't change.
Assuming you haven't created grouping folders to screw up the order, you can get the body by its position in the Outline under geometry:
my_body = ExtAPI.DataModel.Project.Model.Geometry.Children[0].Children[0]
The first "Children" is for the part and the second is the body. If you don't see multibpdy parts, then each body is a singular body in a singular part.
To get Outline objects by name seen in Outline:
my_body = ExtAPI.DataModel.GetObjectsByName('My Body')[0]
Since there can be multiple Oultine items with the same name, the zero index gets the first one.
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