AMEX has a policy that you can only receive the sign up bonus once per lifetime for each card.
That said, there are many different "flavors" of AMEX Platinum cards - each offering essentially the same benefits and you can get the sign up bonus on each of them since they are considered different products. So you really don't have to wait.
Of note, the Ameriprise co-branded Plat, while it offers no sign up bonus, has no fee for the first year and offers the same benefits as the other "flavors". Technically, you're supposed to be an Ameriprise client but that restriction is not enforced.
https://www.doctorofcredit.com/diffe...platinum-card/