It is not uncommon for those who feel they were hit by a Google penalty to submit more than one Google reconsideration request. But does it hurt you to submit multiple requests? Does it slow things down? Do Googlers get annoyed?
About a year ago, Eric Enge interviewed Tiffany Oberoi of Google and one of her recommendations was that you do not submit multiple reconsideration requests. She said, "I don’t recommend sending multiple reconsideration requests in a very short period of time or submitting reconsideration requests for tons of sites all at once rather than one site at a time." She said it can be taken "as a sign of bad faith."
Really? Tiffany is one of those Googlers that sit in the search quality meetings (at least some).
But John Mueller said in a Google Webmaster Help thread:
In general, if you submit a new reconsideration request before a previous one has been processed (sometimes - depending on the issues involved and on the size of the queue - it can take up to a few weeks or more to be processed), then those additional reconsideration requests may be looked at by the web-spam team, but they're generally seen as duplicates and not responded to. Because of that, it's usually best to wait for a response before submitting something new (and even better, to wait until you have something very substantial that was improved before submitting the first reconsideration request).
He doesn't recommend you submit duplicate requests but if you do, generally a Googler will just mark them as duplicates and not bother responding to the duplicates. But sometimes not and someone they may be looked at individually by a Google web spam team member and may lead to a slow down in your request - I assume.
So if you can, try not to submit duplicate requests. Google does a good job now communicating they received the request and sometimes will respond after reviewing them (more often than not these days).
Forum discussion at Google Webmaster Help.
Image credit to BigStockPhoto