Full Idea
Perdurance theory claims that lumps and statues differ modally whilst always being made of the same parts. A natural way to make this less mysterious is for perdurantists to adopt counterpart theory, where objects in different worlds are never identical.
Gist of Idea
Perdurantists can adopt counterpart theory, to explain modal differences of identical part-sums
Source
Katherine Hawley (How Things Persist [2001], 6.2)
Book Reference
Hawley,Katherine: 'How Things Persist' [OUP 2004], p.179
A Reaction
This, of course, is exactly the system created by David Lewis. Personally I rather like counterparts, but perdurance seems a tad crazy.