Wow, if only we all had that problem, huh? But what happens if you do? Since I had to answer this question I thought I'd share my experience just in case it happens to any of you (crossing my fingers for you that it does!). The first thing to remember is that at this point your writing is becoming a career and you have to treat it that way. These folks are kindly asking for your material on which they will spend a considerable amount of their time. That said, we must be courteous to those who have already begun reading our work and have started investing their time.
The last thing you want to do is send the entire manuscript out to everyone who requests it without communicating with those who already have a partial or the entire piece of work. That could be career suicide. Once someone has already begun to read your entire manuscript if another asks to read it, it's a really good idea to ask the first agent if they'd like an exclusive read. Imagine being an agent and reading a potential clients entire manuscript, putting a lot of time and effort into it, and then the client pulls the rug out from under you and says 'thanks but I've been offered representation by someone else'. If they're taking their time to consider our work we need to take the time to be considerate of them.
Does this mean you have to go with the first agent who says yes, especially if others are interested? No, of course not. Finding an agent is like finding a spouse; it can be incredibly difficult to find the right one. However, if you did your research on the agents you submitted to in the first place and didn't just throw out a blanket of query letters, you're already well on your way to finding the right agent. Keep up the communication with any who have asked to read your work, even if you're unable to send it out right away because someone else has asked for an exclusive look. You never know if the first agent will end up passing on the project or offering to take you on.