Other than Delta 360, not officially. That said, I have no doubt that they have some sort of customer value score of which total spend, average fare class, etc is taken into account - and that customer value score may increase the probability of phone agents being generous with exceptions.
It is purely anecdotal but the number of waivers I get without even asking is through the roof compared to when I only spent $17K my first year as Diamond (now I spend $40-50K).