What problems have people been experiencing when using a partition over sda9?
I read it somewhere, but I can't remember the details, or where I read it.
Most Linux distros will work ok in this situation. This is rare.
Is there any other way solve this problem?
Tiny Core is frugally installed. Linux distros which are frugally installed can coexist on the same partition as another Linux distro (some can also be installed on FAT32 and coexist with Windows, but this is not ideal, as FAT32 is more prone to corruption).
Just make sure you don't have any files or directories in the base directory with the same name. For example, if you had /boot/bzImage in both, rename bzImage to something else in one of them, and modify the Grub menu appropriately.
/home and /opt may clash. To test it out, you could rename /home and /opt in the existing distro to something else (it will not work then), and test Tiny Core.
When running, the root directory in Tiny Core (and other frugally installed Linux distros) is actually in ram and the swap partition, so it doesn't clash with the root directory of the other distro on the hard drive.