  We introduce completely semi-$\varphi$-maps on Hilbert $C^*$-modules as a
generalization of $\varphi$-maps. This class of maps provides examples of
CP-extendable maps which are not CP-H-extendable, in Skeide-Sumesh's sense.
Using the CP-extendability of completely semi-$\varphi$-maps, we give a
representation theorem, similar to Stinespring's representation theorem, for
this class of maps which can be considered as strengthened and generalized form
of Asadi's and Bhat-Ramesh-Sumesh's analogues of Stinespring representation
theorem for $\varphi$-maps.
  We also define an order relation on the set of all completely
semi-$\varphi$-maps and establish a Radon-Nikodym type theorem for this class
of maps in terms of their representations.
