And you can certainly do that with no problems. I just used the AAdvantage Shopping portal to buy bras from JCPenny.com, and used my Chase Freedom card to pay for the purchase; I got 3x AAdvantage miles from the shopping portal plus 5x Ultimate Rewards points by using Chase Freedom (as department stores are one of their bonus categories this quarter). Did the same thing last year using the AAdvantage portal to buy Christmas candy from Macy's.

I'll add a card to your list to consider: Chase Sapphire Reserve. Offers 3x points on dining and travel, plus travel insurance and primary rental car insurance coverage, plus a $100 credit when you apply for or renew Global Entry or TSA Pre-check. It has a $450 annual fee, which is NOT waived during the first year, but since it also credits you up to $300 on travel expenses charged to the card yearly, that becomes a $150/year fee. For only $55/year more than the Sapphire Preferred, you earn points faster and get more travel benefits. It's not a card for everyone, but since you sound like you travel a lot, it's one that might make sense for you.