I have 20 open credit cards (4 chase, 5 amex, 3 citi, 3 bank of america, 1 discover, 2 barclays, 1 bank of hawaii, 1 capitalone).

I did cancel two cards (with high limits) in the weeks leading up to my big churn, partly to avoid some annual fees and partly to reduce the amount of credit I already had at two banks. This is contrary to the strategy employed by others: offering to reduce/cancel a card in exchange for an approval. I have also used this strategy with great success.

I figured I probably needed to use both approaches to succeed in my Super-Mega-App-O-Rama. Overall, I think it worked well. I was approved for 11 of 13 cards. The two declines were from Amex (too many applications at once) and Citi (too many inquiries). The question of total available credit came up, but I was able to negotiate trades where needed.