Any PCIe USB3 card (USB3.1 gen. 1) which has a driver in the kernel should work, but if you have multiple ports on it, I’d make sure each port has its own controller and is not just a HUB of multiple ports going to a single controller. Cheaper multi-port cards tend to not use as many PCIe lanes and also tend to have only a single controller. If the card actually wants four PCIe lanes, then chances are quite high each port has its own controller. I don’t have a suggestion on a specific card, and specifications often need detail prior to being able to tell if the card has multiple controllers (and of course a single port card would have only one controller).
A bridge chip is a great way to go if you are building your own carrier board.
If the kernel has the driver for the card (or the card’s chipset), then you’d probably still have to build the kernel module and copy the file to your TX2.