I'm actually thinking of trying to do the same (but not 5X).
I got a 2K starting limit on my BCP. I got my CSP and BCP about a week apart from each other (Chase was first, approved for 5K starting CL). The CSP has now been increased to 10K, so I was going to try for 10K on my BCP as well on my 61st day, hoping AMEX will try to be competitive and approve the 10K, even though the 3X CLI would only allow 6K. I'm hoping if AMEX doesn't approve the 10K they'll counter offer $6000 (wouldn't want to lose that too lol).
***AMEX PLATINUM NPSL *******AMEX BCP 23,100***** CITI DOUBLE CASHBACK $5,900 *****Chase Sapphire Preferred $10,000 **** Chase Freedom $8,000 *****Sears Mastercard Platinum $5,000 **** Macy's Star Rewards $1,000 ***** American Express BCE $24,900 (AU) **** *****Discover IT $8,500 (AU)*****