  We introduce and study a generalization of Schur's $P$-/$Q$-functions
associated to a polynomial sequence, which can be viewed as ``Macdonald's ninth
variation'' for $P$-/$Q$-functions. This variation includes as special cases
Schur's $P$-/$Q$-functions, Ivanov's factorial $P$-/$Q$-functions and the
$t=-1$ specialization of Hall--Littlewood functions associated to the classical
root systems. We establish several identities and properties such as
generalizations of Schur's original definition of Schur's $Q$-functions,
Cauchy-type identity, J\'ozefiak--Pragacz--Nimmo formula for skew
$Q$-functions, and Pieri-type rule for multiplication.
