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Applying for a lot of credit in a short period of time is credit seeking behavior. All banks have policies in regards to it. About 4 month's ago, cap1 cut me off for applications and CLI for too many recent applications. That restriction was just lifted about a week ago. For data points, I have 19 years of credit history and nearly 40 accounts reporting.

A spree of a handful of accounts (say, 3-5) isn't going to cause any red flags on a sound profile. Also keep in mind that with a spree the new accounts aren't actually seen, only the inquiries. With inquiries being spread across the bureaus, seeing a couple of new inquiries IMO isn't going to turn off a potential lender.
Any hard inquiry is considered the persuit of new credit (Credit Seeking). A credit line increase or new credit card account is the persuit of new credit. Keep in mind the way a lender thinks that a consumer is only going to apply for the credit they need. When lender sees multiple inquiries and new open accounts in a short period of time the question becomes is why does this consumer need all that credit? At some point in time this becomes a red flag. My definition of an app spree for me is one card because I researched the cards that meet my criteria and picked the best one in my opinion. I have 6 credit cards total and I could have more but have no use for any more.
It's all relative to the profile that you're seeking credit on. Someone with a 720 score that applies for 3 products isn't going to be viewed the same way as someone with a 620 score. That being said, there's no blanket statement answer to this question/topic.
Like I said in my previous post, against a solid profile a small spree isn't going to draw any red flags or cause anything adverse to happen. On a weaker profile, one may want to think twice before pulling the trigger on such a spree.
@Anonymous wrote:A spree of a handful of accounts (say, 3-5) isn't going to cause any red flags on a sound profile. Also keep in mind that with a spree the new accounts aren't actually seen, only the inquiries. With inquiries being spread across the bureaus, seeing a couple of new inquiries IMO isn't going to turn off a potential lender.
Thanks. I was thinking this would be the case but wanted to verify. I've actually reduced the number of cards I plan to app so will likely only be in the 2 or 3 (max) range. Before I was aiming for 3 or 4. Either way, I looked at previous pulls for all card accounts since I have relationships with all but one. Citi is my only wildcard on who they'll pull but we shall soon see!