There will be times during The Process when you feel like you've hit the wall with your manuscript. You've taken it out to your top 5 (or 50 or 500) agents, they've requested your partial, but then every single one turned you down. What exactly--besides whistling in the dark, of course--are you supposed to do now? Can you revisit these agents again?
Like so many topics, the answers to these questions will vary from agency to agency. I can only answer for us.
First, please don't query us with same project, even if you've revised and/or re-written the manuscript. If we're interested in seeing it again, we'll specifically tell you that when we respond to your partial or full manuscript (I think most agents would say the same thing). This can feel killer, especially if you've had several agents respond with similar comments and you feel like now you're equipped to make your manuscript even better, more polished, totally marketable, etc. However, it's a great argument for not sending your manuscript to every agent in the universe (or multiverses--that's just a side tidbit; I'm fascinated by this concept right now) at the same time. If you send your query and manuscript out in smaller batches and five agents respond with similar comments, you have the opportunity to take those comments back to your manuscript, revise (if you agree with the comments) to a stronger manuscript, and query a new batch of agents.
"Ok, fine, so I won't re-query with the same (or revised) project," you say, "but what about querying new manuscripts?" Querying a new/different manuscript after receiving a rejection on a full or partial is fine for us. Ideally, you'd probably wait a bit (at least a few weeks) before querying again. If we've provided comments with a rejection on your full or partial, consider those in relation to your new manuscript. Do you see any themes, constructions, etc. that might crop up as similar problems in the new manuscript?
When you do query a new project, a brief, polite mention that we previously considered a different manuscript of yours is a good note to include. I always appreciate an acknowledgment that we've had previous correspondence, plus it gives me an opportunity to check back through notes or records on your earlier manuscript if I want.
One note to consider: If we've requested, reviewed and rejected a couple of your manuscripts, you would probably be best served to query other agencies. It's best to end up with an agent who loves your work, your style and your themes, and if we've rejected multiple manuscripts, it's likely that our tastes just don't mesh with yours.
Also, while we're on the topic, here's a reminder to only query one project at a time. Sending us paragraph summaries for 15 unrelated books and asking us to pick which one we want to read is likely to result in an almost InstaReject. We wouldn't pitch your books like that to editors; please don't pitch them that way to us.