Is it possible to make a usb that is bootable on both uefi and bios?

I have a grub4dos multiboot usb drive that contains some tools for computer checking. However, it only works on legacy boot. If you want to boot up from the drive, you need to change the bios to accept legacy boot. Switching between uefi and legacy boot is sometimes trouble or impossible (bios being password locked).

Is it possible to make a usb that is bootable on both uefi and bios?

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