  We present a next-to-next-to-leading order (NNLO) realization of a general
quark mass scheme (S-ACOT-$\chi$) in deep inelastic scattering and explore the
impact of NNLO terms on heavy-quark structure functions $F_{2,L}^{c}(x,Q)$. An
amended QCD factorization theorem for DIS is discussed that validates the
S-ACOT-$\chi$ scheme to all orders in the QCD coupling strength. As a new
feature, kinematical constraints on collinear production of heavy quarks that
are crucial near the heavy-quark threshold are included in the amended
factorization theorem. An algorithmic procedure is outlined for implementing
this scheme at NNLO by using mass-dependent and massless results from
literature. At two loops in QCD cut diagrams, the S-ACOT-$\chi$ scheme reduces
scale dependence of heavy-quark DIS cross sections as compared to the
fixed-flavor number scheme.
