AmEx Platinum pays you $600 a year to have it, why not have multiple? Especially with the $550 annual fee waived for military members per the SCRA.
AmEx will not let you apply for another card that you already own, this goes for multiple Platinum Cards. However you can product change to multiple cards you already own after one year. For example you can get the AmEx Platinum, spend $5k in 3 months for 60,000 MR points:
Then in one year from getting the green, call and product change it to another Platinum for another $200 in flights, $200 in Uber, $100 for global entry, and $100 for Saks 5th Ave credit. The SCRA waiver will continue to cover the new $550 annual fee.