Thomassé's sibling-number conjecture for countable relations

Let $R$ be a relation, with domain a non-empty set and with any fixed finite arity. For a structure $R$, let $Sib(R)$ denote the number of isomorphism classes of structures equimorphic with $R$. Thomassé's conjecture. If $R$ is countable, then

$$Sib(R)=1\text{ or }\aleph_0\text{ or }2^{\aleph_0}.$$

The paper proves this conjecture for countable direct sums of chains, while the assertion for arbitrary countable relations remains open in the supplied context.