Some samples with MadGraph and matching have an emission scale variation.
I think these can just be labeled as PartonShower weights (so LHEPartonShowerWeight, seems contradictory, but I think it's ok).
Example in slide 5: https://www.dropbox.com/s/c17g859p15xpf42/200820_shKo.pdf?dl=0
Need to make sure that parton shower weightgroup features support this.