If an author has several manuscripts ready for submission, how should they handle that? Should they send in the first one, wait until the contract has been signed, and then submit the second? Should they wait until the first book has come out? Or can they submit the second one sooner than that? Is it all right to submit #2 immediately after getting a rejection for #1?
If the books are part of a series, submit the first one and in your query, briefly mention that this is intended to be a series and book #2 is almost complete.
If the books are unrelated, wait until the contract is signed. Then tell your editor/publisher that you have a second book ready and ask when they would like you to submit it. If you're a first time author, they're going to want to see how the first book sells. If you're an established author, they're going to want you to churn them out quickly--1 to 2 per year, if possible.
Some authors are too prolific for the size of their publisher. When this is the case, you'll want to make sure there is a clause in the contract that if they reject a title, you're free to submit to other publishers at any time.
If book #1 is rejected, no, don't immediately (as in the next day) send #2. If the publisher has given an indication of the reasons for rejection, evaluate book #2 within those guidelines. If their reasons have to do with genre, market, or other things specific to the publisher, you'll need to determine if #2 is a better fit for them. If not, submit elsewhere.
If they've talked about structure, technique, plot, characterization, etc., you'll want to rewrite book #2 to clean it up based upon their suggestions before submitting it.
If they've said, "We love this, but it's not right for us. Send us something else ASAP!" then you can send #2 right away.