You seem to be asking for: instead of having a single shell consisting of px, py, and pz orbitals which are just rotated versions of each other, have the px, py, and pz orbitals be fundamentally different with different coefficients.
I have never heard of a basis set that does that, and it seems like a very bad idea. You can change the energy of a system just by rotating it in space.
As far as I know, Psi does not support such a thing. For efficiency reasons, we assume the same coefficients for every orbital in every GaussianShell.