Include covariates on which parallel trends should not condition?

[valentinyverse]

I would like to know if I can include covariates on which parallel trends are not conditioned.

My setting has no anticipation periods, only one group is treated and therefore I have only one time of treatment implementation, and I have an unbalanced panel. I use the function att_gt to estimate the effect of a policy change (from tracked classes to comprehensive classes) in a region on binary individual outcome variables (e.g. school dropout) and I condition the parallel trends assumption on several binary individual time-invariant covariates (e.g. female, nationality, own ability).

Now I want to include another covariate (share of students with high ability in class) on which I don't want the parallel trends to be conditioned on. Further I'd like to get the estimate back for this continuous variable.
I am really unsure, if this even makes sense in this framework. The covariate has only one value per individual, hence is time-invariant.

The model I estimate is:

att_gt(yname = "dropout", 
              tname = "year",
              idname = "region", 
              gname = "first.treat", 
              xformla = ~ability+female + swiss
              ,
              allow_unbalanced_panel = T, clustervars = "region" , data = data