Utilizing multiple wholesalers to quote E&S risks does not typically increase your chances of writing it. Often times brokers/ underwriters have overlapping markets that are available through multiple wholesalers. Up to 80% of markets can overlap between two brokers. Minimizing the number E&S markets that you are approaching will ultimately improve your chances of success. Focus rather on establishing good relationships with your E&S markets to optimize the process.
Retail agencies who are successful typically work with only a few E&S wholesalers, developing their relationship so the wholesaler is confident in the information provided in the submissions they receive, and therefore offers more competitive products. If the E&S provider, however, knows that an agent is shopping the business with a number of its competitors, they are much less inclined to be competitive themselves if they might put effort into the quote but still lose the business over a paltry amount.