We modified the simulation‐based generic ground‐motion prediction equation (GMPE) model proposed by Yenier and Atkinson (2015b) to enable adjustments for the near‐surface attenuation parameter commonly referred to as kappa (). This enhances the usefulness of the model in applications over a broad range of site conditions from hard rock to soil. The new model is developed for magnitudes 3–9.6 and rupture distances up to 1000 km, for peak ground acceleration (PGA), peak ground velocity (PGV), and 5% damped pseudospectral acceleration (PSA) at frequencies from 0.1 to 100 Hz. The proposed scaling term in the GMPE is a function of , magnitude, and stress parameter, and facilitates simultaneous inversion of response spectral amplitudes to estimate best‐fit values of for a specific site condition and region, along with best‐fit values for event stress parameters and regional attenuation. We check the applicability of the modified generic GMPE to the empirical data in California, using the Next Generation Attenuation‐West2 database. We determine an optimal value of 0.04 s for the B/C boundary site condition (travel‐time weighted average shear‐wave velocity over the top 30 m, ) for sites in California, through inversion of response spectral amplitudes from 1 to 20 Hz. The modified generic GMPE formulation provides a fully adjustable model that can be calibrated to the source, path, and site conditions for any region of interest.