I used the latest BIOS Firmware 3602 https://www.asus.com/Motherboards/P8P67_REV_31/HelpDesk_BIOS/
There was unfortunately not enough space, that i deleted a module named: "OnBrdDevDXE"
With the help of this guide, i installed a compressed version of the NVMe module.
Until now I haven’t experienced any limitations or disadvantages of this ROM.
Only the name is not displayed correctly in the BIOS and if the NVMe is the only device(no another SSD) an error message is displayed during the “Post notification” which can be ignored. The system starts anyway.
To understand the whole process of solving my problems, here is a link to my first post. Safely remove DXE Modules without breaking (not enough space) (root volume can’t be grown)
PS: For ASUS P8P67 Pro Rev3.1 Version please use the modification that @clarkwv2 made available. Link
P8P67_REV31-Asus-3602_NVMe-mod.zip (3.23 MB)