Amex used to have a limitation of only one card per type (ie, you could have a credit card and a charge card, but not two credit cards).
This was changed a while ago, and until recently I had three cards (Amex Plat credit / Gold Credit [fee free] and a Qantas Premium). It's now back to two cards though.
On the application form, there may be a box that asks if you want to cancel your old card - of course you don't, so ensure it isn't ticked.
Even when I didn't tick that box, Amex still cancelled my Plat card when I added the Qantas card, and I got them to re-instate it after a few phonecalls.
Assuming both cards are eligible for Membership Rewards, then they will be linked. There might be some dramas if they are of different Membership Rewards types - but Gold Credit and Plat Credit both give points to the same Membership Rewards program, so shouldn't be a hassle.