Perhaps not. Which card do you have Blue for Business or Blue Business Plus?
Blue Business Plus explicitly allows spending above the nominal credit limit:
Very true. I am told I can spend around double my current limit and they will approve the charges. However, I do not want to have it appear that I am maxing out my business cards with AMEX when the utilization would be at 80% +, so I pay it down as soon as the charges hit. It's ridiculous.