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The storage of biometric data has raised significant privacy concerns, necessitating robust measures for secure storage. While traditional Privacy-Enhancing Technologies (PETs), like Cancelable Biometric (CB) schemes, excel at creating protected templates that fulfill criteria such as irreversibility and unlinkability, they often fail to preserve the privacy of soft-biometric information. To address this issue, we propose a hybrid technology that combines PETs, leveraging their different properties to comprehensively address multiple privacy requirements and enhance overall protection for biometric templates. In our approach, we integrate Multi Incremental Variable Elimination (Multi-IVE), a recent technology designed to remove soft-biometric information from biometric templates, with conventional CB schemes. We apply our hybrid technology to facial templates and assess the properties of the resulting protected templates. In the event of stolen secrets, the combination of Multi-IVE with CB schemes helps decrease the accuracy of estimating soft-biometric attributes without affecting recognition performance, compared to CB schemes alone.