Coexistence of preference shock and labor supply shock

Dear Johannes,
In the household utility function of our DSGE model, I have the preference shock in households’ utility maximization problem, and the labor intensity shock/labor supply shock attached to household leisure in the utility function, my understanding is that the preference shock perturbs intertemporal substitution between current utility and expected future utility, whereas the labor supply shock only perturb the leisure component in the utility function. However, I have not yet find a literature which incorporate both the preference shock and the labor supply/intensity shock to support the specification of coexistence of preference shock and labor supply shock, therefore, could I verify with you that is it possible for coexistence of the labor supply shock and preference shock in the DSGE model? and if so, are there any literature have coexistence of preference shock in household utility maximization and labor shock in leisure component of household utility?
Thank you very much and look forward to hearing from you.
Best regards,

Yes, you can have both an inter- and an intra-temporal preference shock. Those are separate concepts. The reason you usually find at most one of those in papers is the fact that preference shocks are frowned upon due to being by definition unobservable.