Write a continuous quine (quine-variant) Let's define a 2-quine as a program that prints its source code two times. For example, if the program ABC printed ABCABC, it would be a 2-quine.
Let's define a 3-quine as a program that prints its source code three times. For example, if the program ABC printed ABCABCABC, it would be a 3-quine.
Let's define a n-quine as a program that prints its source code n times.

Your task is to write a 2-quine, that prints a 3-quine, that prints a 4-quine, that prints a 5-quine, etc...
For example, here is an example of a valid submission (which is fictional of course):
AB

which prints
ABAB

which prints
ABABABABABAB

which prints
ABABABABABABABABABABABABABABABABABABABABABABABAB

etc.
Remember, this is code-golf, so the program with the fewest bytes wins.
QBasic (224 bytes incl. trailing CR+LF)

(Tested with QBasic/MS-DOS on a virtual machine as well as with FreeBASIC with "-lang qb" setting)

a$="a$=:l=l+1:if l&gt;y then f=f+1:y=y*f+y+f:while x&lt;=y:x=x+1:print mid$(a$,1,3)+chr$(34)+a$+chr$(34)+mid$(a$,4):wend":l=l+1:if l&gt;y then f=f+1:y=y*f+y+f:while x&lt;=y:x=x+1:print mid$(a$,1,3)+chr$(34)+a$+chr$(34)+mid$(a$,4):wend