I believe the reason that you cannot have more than one quote at a time is that DU puts a 10 or 14 day courtesy hold on a room for you when you request a quote.
Many of the Disney-specialist agencies do this, to lock in a rate for you, in case you decide to book. Not all of the agencies do this. I know that some people do not care for this method.
Either way, you should be able to contact your agent and explore options!