TUSB8020B: Passing 2-lane DP-Alt signal from host to peripheral

Tool/software:

The above diagram shows a subsystem that I am outlining for a specialty USB-C hub.

I am hoping to expand the number of USB-C 3.2Gen1 Ports by means of the TUSB8020 hub controller, and simultaneously pass a 2-lane DP-Alt signal from the host device to one of the downstream USB-C ports. I am unsure if the TPS65987D can be configured to trigger this signal from the host, if the TPS65988 can advertise that this signal is available to a peripheral, or is this configuration is even allowable under the USB guidelines.
I have worked with the TUSB8020B in the past and paired it with TMUXHS4212IRKSR to make a USB-C to 2 USB-A hub, so I would like to continue using that hub controller for these projects, but I am also seeking recommendations for USB-C Hub control IC's that could consolidate my current parts list (such as a 2:4 mux to replace the 2x 2:1 units I have selected).