I routinely switch between the Delta Gold Optima, Hilton HHonors Optima and Starwood Optima Cards.
Usually to avoid the fees. I would usually cancel the other two and sign-up again after 7 or 8 months and ALWAYS got the bonuses offered.
However, I recently didn't get the 10,000 Delta Points for signing back up for the Gold Card.
When I called, the CSR said since I already got a bonus for the Hilton HHonors card, I was not eligible for this card.
So, I guess I will cancel all my AMEX cards at the same time now and wait 7 months and chose one for the bonus.