I’ve actually done this several times. If the primary OS is Windows 10 you have to remember that the efi partition is going to be the second partition. The first will be a system reserve that Windows creates. I don’t use Windows so I don’t worry about that.
The last time I did this I actually used a 4 port usb hub with 4 128gb flash drives plugged into it. I had the main OS Ubuntu Mate 16.04 installed on the internal drive of laptop, and had 4 other distribution installed each on it’s their flash drive. The only partitions on the flash drives were / and /home. Using the flash drives the efi partition on the internal drive had to be used. This created a few issues during the boot process if the drives were not attached, causing grub to boot to a prompt. The work around was to have separate options in the bios under OS manager to choose from. 1 for external drive only, and one for when the others were attached.
I have done this process in the past using a WD Pasport 1tb external and was able to do the install partitioning and efi partition on the external drive ans well. After install with external drive attached, bios set to with the external drive set before the eternal in the bios boot order I was able to open the bios OS Manager with the external drive connected and choose the loader to boot from. If I chose the external option there were entries in grub as well for the OS on the internal drive. If the option for the internal drive was selected it would be the only OS choice in the grub menu.