There isn't enough to be overpowering at all, imo.
Of course, I'd make the sauce from scratch, thus building the profile as I go, because I think the results are likely to be far superior to what one can come up with via what is, essentially, the 'doctoring up' of a commercial sauce. Commercial sauces are, to me, usually so fraught with ingredient, quality, flavor and volume problems that fixing those requires as much if not more work than just starting anew. Make the sauce with or without any tweaks you see fit and see if it is what you want or if there needs to be changes that might be best made using a from-scratch approach. If not, fine; if so, you'll have a basis that makes sense to you as a starting point in developing a scratch sauce.