Adding random noise to a group level variable

I'm performing multilevel analysis and, to check for statistical artifacts, I want to create new group level variables adding random noise to some group level variables (like school-level socioeconomic composition).

In R, the jitter() function allows to add random noise to a column easily:

jittered_variable <- jitter(variable)

However, this function add different values to a group level variable within groups.

Is there any way in R to add the same random noise to a group level variable within groups? For example, +0.5 for all the members of group 1, -0.3 for all the members of group 2, and so on.