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 factor
ization 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.
