  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.
