  We introduce certain generalisations of the characters of the classical Lie
groups, extending the recently defined factorial characters of Foley and King.
In this extension, the factorial powers are replaced with an arbitrary sequence
of polynomials, as in Sergeev-Veselov's generalised Schur functions and Okada's
generalised Schur P- and Q-functions. We also offer a similar generalisation
for the rational Schur functions. We derive Littlewood-type identities for our
generalisations. These identities allow us to give new (unflagged) Jacobi-Trudi
identities for the Foley-King factorial characters and for rational versions of
the factorial Schur functions. We also propose an extension of the original
Macdonald's ninth variation of Schur functions to the case of symplectic and
orthogonal characters, which helps us prove N\"agelsbach-Kostka identities.
