Summary Bounding surface plasticity models based on one‐dimensional hardening functions are broadly accepted as a valid approach to represent the multiaxial cyclic behavior of undrained cohesive soils. However, under certain conditions, these models may exhibit deviations from the expected stress path. This makes them inadequate to meet traditional hysteretic rules. Current solutions to this problem impose thresholds to help adjust the stress path by introducing additional memory variables. This article presents a formulation that achieves the same goal without the need of such additional variables. The proposed formulation operates on a generic hardening function under multiaxial loading while preserving the simplicity inherited from pure deviatoric bounding surface models. In addition, the approach presented here allows the implementation of Masing‐type rules, as well as the use of reduction factors to mitigate the overdamping effects of large hysteresis loops. The formulation is tested using well‐known hyperbolic backbone functions under radial and nonradial multiaxial loading cycles, and it is shown to have good agreement with reference solutions.