Are commutative digital signature possible?
Let a signed message consist of a bit string $m$ and a set of signatures $\Sigma$.  A ‘signed message’ of a bit string $m$ with no signatures is $(m, \{\})$.  When the $i^{\mathit{th}}$ user signs $(m, \Sigma)$, they return $(m, \Sigma \cup \{\sigma\})$ where $\sigma = \operatorname{Sign}_{S^i}(m)$.  The verifier confirms that there are signatures by all the signers they care about on the message.

This works with any base signature scheme, like Ed25519.  If a signature appendix in the base signature scheme adds $s$ bytes, and there are $n$ signatures, a signature appendix in this composite signature scheme adds $s\cdot n$ bytes, and the cost of verification is at most $s$ times the cost of verification of the base signature scheme.

If this doesn't satisfy your goals, you'll need to be more specific about what they are!