I have a Delta Skymiles AmEx, a Hilton Honors AmEx, a Starwood SPG AmEx, an AmEx Blue, and an AmEx Business Platinum. So in answer to your question, you certainly can have more than one. I've often moved LOC between my personal accounts but it's not allowed to/from the corporate account.
By far the easiest way to get a credit line increase on a particular AmEx card is to respond to one of their solicitations for a new card. As soon as it's received, move all or part of the LOC to the card you wish to increase.