Even better, just get an American Express Platinum Card. It'll give you Global Entry (with Precheck), Priority Pass membership, and $200 in airline credit.
I'm actually about to let my Amex Platinum Card lapse. It's no longer worth the $450/year fee, despite free Global Entry ever five years.
Their points are becoming worthless (Chase has done well in this regard, partnering with United and Southwest), travel booked directly with Amex is usually simple more expensive than other travel aggregators, Costco is dropping taking Amex, etc.
I signed up for a Chase Sapphire Preferred card, and its far superior. Its rental car insurance is first tier/full coverage; I have no need to file a claim with my own insurance ever if I use the card. The rewards are much better, and the yearly fee is only $100.
I put most of my spend on my Chase card as well (they have some great transfer partners, especially for international award flights).
However, for me the $450 fee is easily worth it. The airline fee credit drops it down to $250. And $250 for lounge access + precheck + Boingo + SPG/HHonors Gold is worth it to me. Without those benefits, I'd be tempted to pursue loyalty to an airline and I save well over $250 a year by price shopping.
I'm going to get a Citi Prestige as my next card, which to me works better than Amex Plat - 4th night free on paid hotel stays, Admirals Club access, Priority Pass Select for primary & authorized users (with access to 2 guests free vs. none on Amex Plat), Global Entry and 250$ in flight credit that can be redeemed for airfare vs. incidental charges with Amex. Not to mention, it's easy to get an in-branch offer of $350 a year plus the fact that there's no bonus for everyday spending on Amex Plats.
Depending upon your requirements, some of the other Chase cards are pretty useful as well. Currently you can use their United Club card to get a qualifying dollar waiver on status levels. It's otherwise not as good as the Sapphire but, if you fly a lot of domestic economy on relatively inexpensive routes, the waiver can be good to have.
