Sorry page based on Connection limit

Our application guys are having issues where their connections get exhausted which causes the server to become unresponsive. We've proposed a couple of items which are using connection/rate limits and a sorry page. I know that you can do this with there is no load balancing option available but I was curious if you could present a sorry page when the connection limit has been reached? We would be putting the connection limits and rate limits on the pool members if that helps.

Thanks in advance!