There might be a more straightforward approach but I was able to get this to work. If you run the VBA macro below it will prompt you to select the body you want to break up and will result in creating new bodies for each "lump" and turning off the visibility of the selected body.
Public Sub CreateIndividualBodies()
Dim partDoc As PartDocument
Set partDoc = ThisApplication.ActiveDocument
' Have the body to break apart selected and make sure it has multiple "lumps".
Dim selectedBody As SurfaceBody
Set selectedBody = ThisApplication.CommandManager.Pick(kPartBodyFilter, "Select the body")
If selectedBody.FaceShells.count < 2 Then
MsgBox "The selected body should have more than one ""Lump""."
Exit Sub
End If
' Create a collection to store the individual bodies.
Dim transBodies As ObjectCollection
Set transBodies = ThisApplication.TransientObjects.CreateObjectCollection
Dim features As PartFeatures
Set features = partDoc.ComponentDefinition.features
' Iterate over each of the shells in the selected body.
Dim i As Integer
For i = 1 To selectedBody.FaceShells.count
Dim currentShell As FaceShell
Set currentShell = selectedBody.FaceShells.Item(i)
' Collect all of the faces in the body that are NOT in the current shell.
Dim shell As FaceShell
Dim facesToDelete As ObjectCollection
Set facesToDelete = ThisApplication.TransientObjects.CreateFaceCollection
For Each shell In selectedBody.FaceShells
If Not shell Is currentShell Then
Dim fc As Face
For Each fc In shell.faces
Call facesToDelete.Add(fc)
Next
End If
Next
' Start a transaction and delete the faces.
Dim tran As Transaction
Set tran = ThisApplication.TransactionManager.StartTransaction(ThisApplication.ActiveDocument, "Temp")
Call features.DeleteFaceFeatures.Add(facesToDelete)
' Copy the body in the current state where only the current shell is part of it.
Call transBodies.Add(ThisApplication.TransientBRep.Copy(selectedBody))
' Abort the transaction.
tran.Abort
Next
' Create a base feature for each of the bodies.
Set tran = ThisApplication.TransactionManager.StartTransaction(ThisApplication.ActiveDocument, "Break Lumps")
Dim body As SurfaceBody
For Each body In transBodies
Dim baseFeature As NonParametricBaseFeature
Set baseFeature = features.NonParametricBaseFeatures.Add(body)
Next
' Turn off the visibility of the original body.
selectedBody.Visible = False
' End the transaction.
tran.End
End Sub