Is it possible?

[markspencer]

I have installed Puppy linux currently. Can I boot Puppy Linux with Tinycore as well? Tinycore is not installed currently.

[Juanito]

Your boot loader will be able to boot multiple versions of linux.

Typically you would install different versions of linux on different hard disk partitions, but you could also boot tinycore from within the puppy partition or from cd, usb stick, etc.

Take a look at the wiki section on installing tinycore.