  In this paper we compare outcomes of some extended phantom-like cosmologies
with each other and also with $\Lambda$CDM\, and $\Lambda$DGP. We focus on the
variation of the luminosity distances, the age of the universe and the
deceleration parameter versus the redshift in these scenarios. In a dynamical
system approach, we show that the accelerating phase of the universe in the
$f(R)$-DGP scenario is stable if one consider the \emph{curvature fluid} as a
phantom scalar field in the equivalent scalar-tensor theory, otherwise it is a
transient and unstable phenomenon. Up to the parameters values adopted in this
paper, the extended $F(R,\phi)$-DGP scenario is closer to the $\Lambda$CDM
scenario than other proposed models. All of these scenarios explain the
late-time cosmic speed-up in their normal DGP branches, but the redshift at
which transition to the accelerating phase occurs are different: while the
$\Lambda$DGP model transits to the accelerating phase much earlier, the
$F(R,\phi)$-DGP model transits to this phase much later than other scenarios.
Also, within the parameter spaces adopted in this paper, the age of the
universe in the $f(R)$-DGP model is larger than $\Lambda$CDM, but this age in
$F(G,\phi)$-DGP is smaller than $\Lambda$CDM.
