Stochastic ground motion simulation models are often less accurate at lower frequencies than at higher frequencies when fitting recorded data unless supplemented by a deterministic forward directivity velocity pulse model. Moreover, time-modulated stochastic models, which adjust ground motion amplitudes over time, typically use functions that fail to capture multiple strong-motion phases. The February 2023 Turkey (Türkiye) earthquake exhibited diverse recordings, including near-fault and far-field motions with pulse-like and non-pulse-like characteristics, along with single and multiple strong-motion phases. To better represent such a diverse set of recordings, this study enhances a fully non-stationary site-based stochastic model without combining it with a deterministic model. Improvements include a new band-pass filter with upper- and lower-frequency limits, which refines the representation of the low-frequency content. Moreover, a time-modulating function that can represent energy arrival in multiple strong phases is introduced. The reference model’s parameters are identified by fitting to the energy content, zero-level crossings, and cumulative counts of positive-minima and negative-maxima of a target accelerogram. This fitting procedure is modified to address the increased number of parameters. These improvements broaden the reference model’s applicability while preserving its simplicity, a key aspect appealing to engineering practitioners. The improved model’s applicability is demonstrated by simulating a dataset from the February 2023 Türkiye earthquake, and the accuracy is tested using a pulse-like Next Generation Attenuation Relationships for Western United States dataset. Validations are performed based on total energy, zero-level crossings, Fourier amplitude spectrum, elastic response spectra, and peak ground motion parameters. Validations are performed schematically in the time and frequency domains and quantitatively using goodness-of-fit scores, various validation-metrics errors, and inter-period correlations. Overall, the improved stochastic model can effectively simulate a set of diverse ground motion recordings, including near-fault pulse-like records, records with multiple strong phases, and far-field motions across a broad frequency range.