The slush pile is simply an inbox (usually) containing submissions from writers without an agent. There is no way you can avoid it. The agents' office is where the slush pile lives. Publishers won't even look at a manuscript unless it comes via an agent or a recommendation from a colleague, so they don't have a slush pile.
You can send out multiple submissions but you need to follow the guidelines on the agents' websites to the letter. Don't bother sending anything unless it's complete. Each agent will state what they want you to send and it's time consuming getting it right. Don't ever send a generic email - it will signal you are an amateur.
Look at the agencies' websites. Find an agent within the agency and send them a personalised email, stating why you are applying specifically to them. This might be because of their interests or because of the authors they represent.
Don't compare yourself to a well known writer. Don't say your book would make a good film. Don't say your friends like it. Don't say it gets better as the book progresses.
Only send what they state they want. Read the instructions carefully. If you email one agent and call her by another agent's name, you can forget it. If you send the whole book instead of three chapters, forget it. If you don't send a covering, personal email, forget it.
Keep a record of who you've sent your work to and what exactly you've sent them. Don't send them three chapters then start to fiddle around with the three chapters - if you do this, save it under a different name. I found it easier to name each document eg Chapters 1-3 of X,Y,Z for John Smith. You know, then, exactly what they've seen.
One agency (Johnson & Alcock) asked for the following questions to be answered - I found it a really useful thing to do, but really difficult.
- Give us your best sales pitch and sound bite - in one sentence how would you sell your book/idea to a publisher?
- Give us your two to three sentence summary of what your book is about.
- Tell us in two to three sentences about the intended audience and whether there are any useful comparisons you would make with other books and authors.
- Tell us about yourself - again in two to three sentences.
- If you have already published the work independently or through a third party online, e.g. Amazon, tell us how it has gone so far. We love (accurate) hard figures and statistics!
- Let us know if your proposal is with other agents/agencies and/or publishers.