Portenta H7 POE?

Using the shield: Portenta Vision Shield - Ethernet — Arduino Online Shop
Can I power it POE?
Could I use one set of Portenta H7 and Eth shield to power a second set?

I'm trying to power one of them just through ethernet. The other I can connect to Vin. Is that possible?

Based on the schematic, it maybe looks like It does not have POE. But should be possible if I create a custom hat for it, or am I missing something?

I will be trying to make a POE carrier board in the near future, but I would use a 1G POE plug and not a 100MB one. This way the X8 (or any future compatible boards) can rest on the same carrier board.

I will use this power supply

] Ag9905LP Silvertel | Mouser Canada

And probably this connector

85789-1001 Molex | Mouser Canada