In the past, we have discussed the admissions myth that when a school that has placed you on its waitlist says that it wants no more/new information from you, this is some kind of “test,” and you should supply additional materials anyway. This is patently not true. Similarly, candidates waitlisted at programs that say they are open to important additional communication should not interpret this to mean constant communication. The difference is significant.
As is the case with any waitlist situation, before you do anything carefully read the waitlist letter the admissions office sent you. Frequently, this will include a FAQ sheet. If the school permits candidates to submit additional information but offers no guidance with respect to quantity, this does not mean that you should start flooding the committee with novel information and materials. If you have another potential recommender who can send a letter that highlights a new aspect of your profile, you can consider having him/her send one in, but you should not start a lobbying campaign with countless alumni and colleagues writing on your behalf. Similarly, you could send the school an update email monthly, every six weeks, or even every two months—the key is not frequency or volume but materiality. If you have something important to tell the admissions committee that can help shape their perspective on your candidacy (e.g., a new project, a promotion, a new grade, an improved GMAT score, a campus visit) then you should inform them. If you do not have such meaningful information to share, then a contrived letter with no real content will not help you. Just because you know others are sending letters, do not feel compelled to send empty correspondences for fear that your fellow candidates might be showing more interest. They just might be identifying themselves negatively via their waitlist approach.
Take a step back and imagine that you are on the admissions committee and you have one candidate who keeps you up to date with a few thoughtful correspondences and another who bombards you with empty updates, emails, and recommendations that do not offer anything substantive. Which would you choose if a place opened up in your class? Your goal when you are on the waitlist is to remain in the good graces of the admissions committee. Remember, they already deem you a strong enough candidate to take a place in their class, so be patient and prudent, as challenging as that may be.