# Interaction within*between in mixed models: slope of the within factor as random or not?

I am struggling with conceptual understanding and analytical choice in mixed models.

In a within-subject experiment (2 conditions, factor X), I want to test if the effect of the condition on the outcome response (Y) is influenced by a third variable measured at the subject level (moderator W, at between level).

Thus I coded: fit<-lmer(Y~X*W+(1|Subject), data)

Should I allow the slope of the condition (X) to varying in each of the subjects --> (1+X|Subject)?

Would not the variance of the interaction with the between-level moderator (W) be already explained (at least partially) and concealed by the inclusion of the random slope?

If I understood well, the inclusion of the random slope would take from the residual variance all the variance due to unconsidered subject-level variables, including the variance due to the moderator W.

I hope I could explain my doubts clearly... Thank you