Answer
Yes.
Work Step by Step
$dh=c_pdT+\left(v-T\left(\frac{\partial v}{\partial T}\right)_P\right)dP$
Using $\dfrac{\partial^2 M}{\partial x\partial y}=\dfrac{\partial^2 M}{\partial y\partial x}$
$\left(\dfrac{\partial c_p}{\partial P}\right)_T=-T\left(\dfrac{\partial^2 v}{\partial T^2}\right)_P$
With the relation above we can calculate the change in heat capacity with pressure.
