I have a dual-boot VMware VM that has both 32-bit and 64-bit cores. What I haven't seen mentioned is that you need to have separate 32 and 64 bit tce directories. Here is my extlinux.conf and /mnt/sda1 dir structure:
DEFAULT tc64
UI menu.c32
PROMPT 0
TIMEOUT 600
ONTIMEOUT core
F1 f1
F2 f2
F3 f3
F4 f4
MENU TITLE TinyCorePure64
MENU MARGIN 10
MENU VSHIFT 5
MENU ROWS 4
MENU TABMSGROW 14
MENU TABMSG Press ENTER to boot, TAB to edit, or press F1 for more information.
MENU HELPMSGROW 15
MENU HELPMSGENDROW -3
MENU AUTOBOOT BIOS default device boot in # second{,s}...
LABEL tc32
MENU LABEL Boot TinyCore
TEXT HELP
Boot TinyCore
ENDTEXT
KERNEL /boot/vmlinuz-core32
INITRD /boot/core32.gz
APPEND loglevel=3 vga=791 syslog noswap tce=sda1/tce32
LABEL tc64
MENU LABEL Boot TinyCorePure64
TEXT HELP
Boot TinyCorePure64 with Embedded X/GUI extensions.
ENDTEXT
KERNEL /boot/vmlinuz64-corepure64
INITRD /boot/rootfs64.gz,/boot/modules64.gz
APPEND loglevel=3 vga=791 syslog noswap tce=sda1/tce64
LABEL core
MENU LABEL Boot Core (command line only).
TEXT HELP
No embedded X/GUI extensions are loaded. User extensions scanned or specified
will be loaded, and will need to provide X/GUI if required.
ENDTEXT
KERNEL /boot/vmlinuz64-corepure64
INITRD /boot/rootfs64.gz,/boot/modules64.gz
APPEND loglevel=3 vga=791 text base syslog noswap tce=sda1/tce64
/mnt/sda1/boot
/mnt/sda1/boot/extlinux
/mnt/sda1/tce64
/mnt/sda1/tce64/ondemand
/mnt/sda1/tce64/optional
/mnt/sda1/tce32
/mnt/sda1/tce32/ondemand
/mnt/sda1/tce32/optional
/mnt/sda1/lost+found
I moved boot up so it wouldn't be in either tce directory. I wouldn't think it would take much to modify the install scripts to set this structure up (or something like it).