The Bounding Surface (BS) plasticity model for metals is modified according to the proposition introduced in the works of Burlet and Cailletaud (1986) and Delobelle (1993) for the kinematic hardening of a classical Armstrong/Frederick (AF) model, called the BCD modification from the initials of the foregoing authors. The BCD modification was introduced in the relative kinematic hardening between Yield Surface (YS) and BS, unlike its introduction in the absolute and single kinematic hardening of YS for an AF model, hence, achieving two objectives: first, maintaining the inherent feature of BS for decoupling plastic modulus and direction of kinematic hardening, and, second, allowing a flexibility as to the relative kinematic hardening direction without altering the value of the plastic modulus, a property of BCD modification. In addition, the introduced BCD modification for the BS is significantly modified itself, by introducing a properly varying modification parameter instead of the fixed one used in the original works. This simple feature of the novel BCD modification provides a dramatically improved capability to simulate multiaxial ratcheting (MR), because it affects directly the changing flow rule direction, due to the relative kinematic hardening, during complex multiaxial loading, without sacrificing accurate simulations under uniaxial ratcheting (UR) since the plastic modulus is not affected. An additional significant contribution to successful UR simulations is provided by the free-to-choose kinematic hardening of the BS, since the BCD modification is applied only to the relative kinematic hardening between BS and YS. The new model, named SANIMETAL-BCD, is shown to yield superior or equal simulations of UR and very complex MR experimental data for three Carbon Steel specimens, in comparison with other models, within a much simpler constitutive framework. Shortcomings and future necessary improvements are discussed in details. •The multiaxial formulation of a modified bounding surface plasticity is presented.•A novel BCD modification is presented.•The new model, named SANIMETAL-BCD is validated against uniaxial and multiaxial ratcheting experiments.•A discussion about the model’s capabilities and limitations is finally presented.