You can have as many Amex cards as you qualify for. But you can only have so much credit from the company, so each card may be limited in purchasing power. But I've heard they'll let you move the credit limits around from card to card.

Also, Gary Steiger (FT handle pgary) says he alternates every year between Delta and Starwood, taking advantage of fee free first year offers.

I find it simplest and most advantageous to just stick with the always free HHonors Platinum card.