Chase is the only one with 5/24. If you have any other Amex card in good standing and are willing to pay the annual fee, it would be exceptionally rare to see a denial. Make sure your targeted offer is for the 100k SUB first, though. If not, make sure you sign up through a link that is offering it.
5/24 is specifically a Chase rule. The only rule you have to worry about with the info you provided is that AMEX has a once-in-a-lifetime rule meaning once you get a card you can't get any future SUBs associated with the card ever again. So, in this instance getting the 100k SUB for the Plat is defintely worth getting as it's as good as it's gonna get for you.
Edit: fingers slow tonight. 
@simplynoirwrote:Edit: fingers slow tonight.
Not slow, but we've been doing this for days. Alone, we're helpful. Together, we're super helpful. 
@K-in-Bostonwrote:
@simplynoirwrote:Edit: fingers slow tonight.
Not slow, but we've been doing this for days. Alone, we're helpful. Together, we're super helpful.
Double (triple with the third poster) verification is always nice lol.
A simple "you complete me" would suffice. 
Oh, back on topic... there are certainly some rules with the number of cards that you can get from Amex in a particular length of time and other lenders like BoA also have rules like that.
(Happy now?)
Well, for AMEX purposes the only rule that would apply to OP's situation is the 2/90 rule which they can't apply for more than two revolvers in a 90 day period. I can't recall if this also includes charge cards as well.