We review a dynamical dark energy model scarcely studied in the literature and we introduce two possible generalizations. We discuss separately the behavior of the original model and a minimal extension of it by exploring some early and late times limits, we find that the cosmic components are related by their parameters state. In order to have access to the phantom regime we present two dark energy densities inspired from the holographic approach and from the emergent entropic forces model in the early universe. For the first case we obtain a type-III singularity and in the second proposal we have a transition from decelerated to accelerated cosmic expansion that starts as phantom type. However, the final stage of the universe is a de Sitter state.