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As far as I can tell, you can transfer limits between any cards. You are correct about the PC, though.
I recently opened an Amex Hilton Surpass card and transferred $20,000 from my BCE to it. It was pending for a few days, but went through without a hitch.
I've heard varying numbers from people, but the most recent and most common seems to be that $1,000 needs to remain on the donating card.
I kept $5k for cushion reasons. I don't anticipate using the BCE at any point in the near future, but if something happens and it's the only card handy, I don't want to have such a low balance that I end up with a high utilization if it reports.
My BCP card was less than 1 month old and I moved 7k from my Delta Gold to that card with no issue.
There have been some changes on this. In the past I believe the donor card had to be 13 months old and recevier card had to be 6 months. However there has been numerous posts on here about getting that done sooner without issues. Also it had been reported recently that AMEX requires 1k to be left on donor card. In the past 6months. It may come down to relationship with them. Good luck!!
My SPG got reduced APR, currently 10.49%. It is also on a 12-month promotional APR this year of 6.99%. Originally $10k limit.
I tried to move $10k from my EDP $15k limit, a month ago to the SPG, to make the SPG $20k, the EDP to be $5k. Four days straight I got the message "our systems are updating, try again in 24 hours. I tried again at the end, moving only $5k and that was accepted instantly, SPG to $15k, EDP to $10k.
I suspect there are additional possible limits about how much they want to allow, when moving limit to a relatively low APR. When I moved $8k from my Hilton card of $10k, to make my Delta card $20k, the Delta card has the 19% APR, so they were probably quite happy with that shift.