The duplicate command returns a reference to the new copy. So you just need to store it somewhere.
Try this:
Code:
tell application "Finder"
set file_list to {the path to me}
repeat with i from 1 to 5
set file_list to file_list & {(duplicate file_list)}
end repeat
end tell
Curly braces are how you make with lists in AppleScript. So first you make a list with one object, then you duplicate that list and append to it. Repeat as desired.
The result is 32 copies of the script, since it doubles the number 5 times over (2^5=32).