Javascript ES6 (REPL), 55 bytes

var a=-~a;$=_=>`var a=-~a;$=${$};$();`.repeat(a+1);$();

Saved 2 bytes thanks to @user81655! #Explanation Here's the standard quine framework:

$=_=>`$=${$};$()`;$()

You should be able to see this framework inside the submission. More explanation below.

var a=-~a;

This is the counter, defaulted to 1. Basically, it tells us how much to repeat the quine and increments at the same time.

$=_=>`var a=-~a;$=${$};$();`.repeat(a+1);$();

This is the quine part. We essentially repeat the quine string by the counter+1. Subsequent function calls will override the output.

Javascript ES6 (REPL), 55 bytes

var a=-~a;$=_=>`var a=-~a;$=${$};$();`.repeat(a+1);$();

Saved 2 bytes thanks to @user81655!

Explanation

Here's the standard quine framework:

$=_=>`$=${$};$()`;$()

You should be able to see this framework inside the submission. More explanation below.

var a=-~a;

This is the counter, defaulted to 1. Basically, it tells us how much to repeat the quine and increments at the same time.

$=_=>`var a=-~a;$=${$};$();`.repeat(a+1);$();

This is the quine part. We essentially repeat the quine string by the counter+1. Subsequent function calls will override the output.

Javascript ES6 (REPL), 55 bytes

var a=-~a;$=_=>`var a=-~a;$=${$};$();`.repeat(a+1);$();

Saved 2 bytes thanks to @user81655! #Explanation Here's the standard quine framework:

$=_=>`$=${$};$()`;$()

You should be able to see this framework inside the submission. More explanation below.

var a=a||1;

This is the counter, defaulted to 1. Basically, it tells us how much to repeat the quine.

$=_=>`var a=a||1;$=${$};$();`.repeat(++a);$();

This is the quine part. We essentially increment the counter and repeat the quine string based on the counter. Subsequent function calls will override the output.

Javascript ES6 (REPL), 55 bytes

var a=-~a;$=_=>`var a=-~a;$=${$};$();`.repeat(a+1);$();

Saved 2 bytes thanks to @user81655! #Explanation Here's the standard quine framework:

$=_=>`$=${$};$()`;$()

You should be able to see this framework inside the submission. More explanation below.

var a=-~a;

This is the counter, defaulted to 1. Basically, it tells us how much to repeat the quine and increments at the same time.

$=_=>`var a=-~a;$=${$};$();`.repeat(a+1);$();

This is the quine part. We essentially repeat the quine string by the counter+1. Subsequent function calls will override the output.

Javascript ES6 REPL, 57 bytes

var a=a||1;$=_=>`var a=a||1;$=${$};$();`.repeat(++a);$();

Here we go... #Explanation Here's the standard quine framework:

$=_=>`$=${$};$()`;$()

You should be able to see this framework inside the submission. More explanation below.

var a=a||1;

This is the counter, defaulted to 1. Basically, it tells us how much to repeat the quine.

$=_=>`var a=a||1;$=${$};$();`.repeat(++a);$();

This is the quine part. We essentially increment the counter and repeat the quine string based on the counter. Subsequent function calls will override the output.

Javascript ES6 (REPL), 55 bytes

var a=-~a;$=_=>`var a=-~a;$=${$};$();`.repeat(a+1);$();

Saved 2 bytes thanks to @user81655! #Explanation Here's the standard quine framework:

$=_=>`$=${$};$()`;$()

You should be able to see this framework inside the submission. More explanation below.

var a=a||1;

This is the counter, defaulted to 1. Basically, it tells us how much to repeat the quine.

$=_=>`var a=a||1;$=${$};$();`.repeat(++a);$();

This is the quine part. We essentially increment the counter and repeat the quine string based on the counter. Subsequent function calls will override the output.