I never 4bet PF with JJ+ unless opponent is a spewtard and his 5bet range/4bet calling range is still behind QQ/JJ.

"why would I do this against solid TAGG"
well, um, because he should fold KsKx which is what he should have on the turn like 95% of the time.

BTW, I think I do this with AQ too to tell the truth, so my range does include more hands that beat him that I first thought.