  We introduce a ring of noncommutative shifted symmetric functions based on an
integer-indexed sequence of shift parameters. Using generating series and
quasideterminants, this multiparameter approach produces deformations of the
ring of noncommutative symmetric functions. Shifted versions of ribbon Schur
functions are defined and form a basis for the ring. Further, we produce
analogues of Jacobi-Trudi and N\"agelsbach-Kostka formulas, a duality
anti-algebra isomorphism, shifted quasi-Schur functions, and Giambelli's
formula in this setup. In addition, an analogue of power sums is provided,
satisfying versions of Wronski and Newton formulas. Finally, a realization of
these noncommutative shifted symmetric functions as rational functions in
noncommuting variables is given. These realizations have a shifted symmetry
under exchange of the variables and are well-behaved under extension of the
list of variables.
