Severe punch-through of jack-up rig foundations can occur due to the presence of a stronger sand layer in a bed of relatively soft clay. Analytical estimation of the bearing capacity and leg load–penetration response on such multi-layer stratigraphies is challenging. Accurate mechanism-based models need to be established in each of the layers involved and the effects of the mechanisms in each of the layers on the response in the other layers must be captured. Based on the recently developed failure stress-dependent punch-through models for sand–clay stratigraphies, an extended model is proposed for clay–sand–clay stratigraphies. Half-spudcan particle image velocimetry centrifuge tests and full-spudcan centrifuge tests are used in developing and validating the extended model. The centrifuge test results were discussed in a companion paper and this paper focuses on the analytical developments and prediction assessment. Both spudcan peak resistance (qpeak) and spudcan punch-through depth (dpunch) can be estimated using the model. The predictions by the extended model and by the current industry guidelines are compared against the centrifuge test data. The extended model proposed in this paper outperforms the approaches suggested in the guidelines. An advantage of the proposed approach is that it can be used for either sand–clay or clay–sand–clay scenarios and exhibits excellent performance compared to the model testing dataset considered in this work for both cases. The resulting penetration resistance model is a useful design tool for routine punch-through risk assessment.