Let \({\mathbb{V}}\) be a variety of algebras. The set I\({\mathbb{V}}\) of isomorphism types of \({\mathbb{V}}\)-algebras together with the quasi-order \(\leq\) defined by the condition \(a\leq b\) iff any algebra of isomorphism type a can be embedded into some algebra of isomorphism type b, is called the embeddability skeleton of \({\mathbb{V}}\). The following theorem is proved: If \({\mathbb{V}}\) is a discriminator variety of finite signature which is not locally finite, then every countable partially ordered set can be isomorphically embedded into the skeleton of isomorphism types of countable algebras from \({\mathbb{V}}\).