The big three, Random House, Penguin, and Harper Collins, (listed in order of size) control 75% of the US bestseller market between them. Each has many imprints and you sell to the imprint, not to the "company."
So, for example, you could query half a dozen editors in different imprints of Random House. They will all bid agressively against one another, but there are some rules.
1) All the big houses have divisions. For example, here are Random's divisions
http://www.randomhouse.biz/ourpublishers/ If you scroll down their list, you'll see Crown - my division. You could query Doubleday and Crown because they are separate divisions, and each could offer a bid for your book. You can't query multiple editors within a division and have them bid against one another, though you can have them review the book and choose between them.
2) If two companies are bidding, say Penguin and RH, bids can run free. If you have an auction situation, and the top bidders are from the same company (example: Doubleday and Crown) you have to stop the bidding and choose a winner per the policy of the major houses.
If these houses are your target there are advantages to a long established agent in the City.