Clarifications have been made to this post. Please re-read.
Can you submit the same manuscript to multiple publishers at the same time?
This is called simultaneous submissions. Some publishers accept them, others do not. Check your publisher’s submission guidelines. If the publisher you want to submit to accepts simultaneous submissions, then yes, you can send your manuscript to them, and to other publishers, who also accept simultaneous submissions, at the same time. If the publisher you want to submit to does not accept simultaneous submissions, then you must submit to them, wait for them to reject it, and then submit to the next publisher on your list.
The reason some publishers choose not to accept simultaneous submissions is because then they can read at their leisure without worry that someone is going to beat their time. This is unfair to the author, as single submissions can kill you. For example, let’s say you have 10 publishers on your A list and you have to query and submit to them sequentially. And let’s say they each take about 6 months to go through the review process. It could take you 5 years to get through them. Who has time for that?
Personally, I think there should be a law that forces all publishers to accept simultaneous submissions. But until there is, you have to play by their rules. If they say they want exclusive looks, and you want them to consider you, then you have to send it to them and no one else until they make a decision.
One more word: If you decide to do simultaneous submissions to publishers who accept them, let the publisher know in the query letter that you have submitted to others as well. You don’t need to tell him/her who else you’ve submitted to, but it is polite to let them know that others are looking at it also. And if you get accepted somewhere, write or e-mail all other publishers who are still reviewing your manuscript and let them know it’s off the market.