Sorry to necromance this old thread, but wanted to save someone from tearing their hair out with the comment about YUMI and the TinyCorePure64 iso..
My friend was over today and he was not able to boot any of the many many ways be tried to build the UEFI. we even tried to use YUMI UEFI but had no luck there either.
Yumi-Uefi *used* to work just fine with TCPure64 iso. Yes, for me it was a convenient crutch to use as the bootloader front end replacement for the iso on very strict UEFI only machines.
Later version of yumi-uefi seemed to stop working with TC64, but that was due to an error of using duplicate pathnames in the rewritten tinycore grub.cfg. If you didn't know about it, and since it looked almost exactly like the original, that duplicate path could be hard to spot. I spotted it, and since the the filesystem was no longer a read-only iso9660, it was easy to edit out that mistake.
The most recent versions seems to have dropped TC support altogether as it no longer appears in the dropdown list of supported distributions, nor does the "try unlisted distro" appear to work.
One which performs similarly to yumi-uefi, and has been recently tested by myself is multibootusb v 9.2. Albeit I don't use it to multiboot.
Again sorry - but just wanted to save someone the time and trouble trying to use a 3rd party bootloader that has dropped support for TC.