No American Express (USA) card is broadly churnable. YOU can get the bonus again if you apply through that specific offer. Targeted offers without the exclusion are not rare, but be sure to make and save a copy of the full terms of the offer INCLUDING the terms displayed on the application itself.
the public offer (25k MR for $2000 spend) terms state that the welcome bonus was only for those who didn't have the card before. The offer found in my Amex profile did not include any such language