I want to use an IC that will take x4 3.0 PCIe lanes, and adds a USB 3.1 controller.

This ASMedia one looks ideal, but doesn't appear to be available to the common folk: https://www.asmedia.com.tw/product/E0CYQ4fSpaQxdjzA/f32YQ14SmApn1wNA

There's also https://www.ti.com/lit/ds/symlink/tusb7340.pdf - but that costs 22USD with LCSC, as well as being much slower (only using x1 lane)

I'm finding it hard to Google as well, because it seems to bring up complete products rather than ICs.

Can buy a whole card on eBay with the ASM3242 on it!

Can anyone help here please?