No, Puppy can be installed on the same partition as Ubuntu and I will redo
this. Right now I do not have Ubuntu on my PC, I switched to Dreamlinux.

Puppy, DSL and FreeDOS can even be installed on a flash drive, so you can have
3 OSes on a flash drive.
Configuring Grub in this case is quite easy. For these 3 OSes on the flash
drive the menu.list file looked like this:
default 0
timeout 10
title DSL
root (hd0,1)
kernel /linux24 ramdisk_size=100000 lang=us quiet vga=791 frugal
initrd /minirt24.gz
title Freedos
root (hd0,0)
makeactive
chainloader +1
boot
title Puppy Linux 400 frugal
rootnoverify (hd0,0)
kernel /puppy400/vmlinuz pmedia=idehd psubdir=puppy400
initrd /puppy400/initrd.gz

I slammed the Puppy installation right on the FAT32 partition on which FreeDOS
was.
Unfortunately right now I do not have the stick.

For installing DreamLinux and FreeDOS on separate partitions
on a SATA drive and also being able to boot Windows 2000
installed on another hard drive I modified the menu.list file
(I also modified some OS titles for reasons of mockery and as an
intention of surprise for somebody):

# created by menulst_create.rb
#
default 0
timeout 5
gfxmenu (hd0,1)/boot/grub/message.dream
#
title Ezer furge falank teknosbeka a szilvafan
root (hd0,1)
kernel /boot/vmlinuz-2.6.28.5-1-i686-dream root=/dev/sda2 vga=791
splash=silent,fadein,theme=default console=tty1 ro quiet
initrd /boot/initrd.img-2.6.28.5-1-i686-dream

title Dreamlinux (sda2, mbr) (recovery mode)
root (hd0,1)
kernel /boot/vmlinuz-2.6.28.5-1-i686-dream root=/dev/sda2 ro quiet single
initrd /boot/initrd.img-2.6.28.5-1-i686-dream

title Dreamlinux (sda2, mbr) (memtest)
root (hd0,1)
kernel /boot/memtest86+.bin
quiet

# This is a divider, added to separate the menu items below
title Other operating systems:
root


title FreeDOS cel bengos
root (hd0,0)
chainloader +1
makeactive
boot


title Windows 2000 cel usurel si sprinten
root (hd1,0)
chainloader +1
makeactive
boot