Simultaneous Submissions
You can learn whether a market accepts these (and whether they accept reprints, and much else) from their guidelines.
The first thing to know is that publishing is a buyer's market. That this is an unhappy thing for the sellers (we writers) should be obvious.
Next, you need to know that if a work is publishable by one it is publishable by many.
When a publisher buys a book, it isn't just some editor somewhere who reads it, loves it, and buys it all in the same day.
That editor will have to present the book to an editorial review board, pitch it to the publisher, work out a profit and loss statement, and find a hole in the schedule (arrived at with the other editors). Those other things will have to happen before the offer is made. If those things are done for a book that's no longer available (since if it is publishable by one it's publishable by many, the same process may be happening or already have happened across town), that's time and money wasted, alone with the editor's prestige among the other editors at the house.
Thus, publishers do not like simultaneous submissions. If you simsub and you're good enough to be published I guarantee that you'll be caught. (If you aren't good enough to be published, no one will ever know.)
The exception to this is the auction. This is agent territory. If you have a hot book by a hot author, the agent may select a few publishers who are likely to Really Want This Book, call them on the phone, and say "I'm auctioning this work." What that means is that the one who comes up with the best offer is allowed to publish it. Happy you! (Unless the book subsequently tanks, then Unhappy You, and it's time to pick a nice pseudonym.)