Two kinds of parthood?

I want to explore the thesis that every plurality has a fusion. Suppose that we live in a non-gunky materialist world where everything bottoms out in particles, with all particles being simple. Assume:

1. A fusion cannot gain or lose parts.

2. A fusion continues to exist if all its simple parts do.

3. Parthod is transitive.

4. I can gain and lose simple particles.

Now let F be the fusion of me, who I suppose am made of multiple particles, with some particle P₁ outside of me. Suppose now that the following happens: I, all my particles and P₁ all continue to exist, but a new particle P₂, distinct from P₁, additionally comes to be a part of me. Then by (2), F continues to exist, since all of F’s simple parts do. By (1), I continue to be a part of F. By (3), P₂ will be a part of F. But that violates (1).

(This is not a new argument—I vaguely remember seeing something like it.)

Maybe if we accept the universality of fusions, then the sense of “part” that goes along with fusions—the sense of part in (1), (2) and (3)—is different from the ordinary sense of “part”, as when I say that my kidneys are a part of me. Let’s talk of these as f-parts and o-parts. If we do that, then we can block the argument: P₂ comes to be an o-part of me in but one cannot infer that P₂ comes to be an f-part of F, since f-parthood is transitive and maybe o-parthood is transitive, but an o-part of an f-part need not be an f-part.

That doesn’t quite solve the problem. Let’s keep on elaborating the case. Suppose that I am a material object, and I eventually exchange all my particles, but these particles continue to exist outside of me. Then by (2), F continues to exist. Moreover, by (1) I continue to be an f-part of F. But interestingly, none of my particles are f-parts of F: for the particles I now have weren’t a part of F, since they were neither o- nor f-parts of me initially, and fusions don’t gain parts. Now suppose one of my particles were an f-part of me. Then by transitivity of f-parthood, that particle would be an f-part of F, which I argued it’s not. So none of my particles is an f-part of me.

This is very weird: I’m made of particles, but no particle is an f-part of me. It seems I am f-simple. (There are some alternatives, but they are also very weird.) But presumably if this is true after the exchange of particles, it’s true before—my f-simplicity status shouldn’t change in life. So I’m always f-simple, even though I have many proper o-parts, say my particles.

It’s now looking like f-parthood is very different from o-parthood, and I wonder if it’s a kind of parthood at all.