I was just wondering how this would be ruled, if a creature is grappling another creature, what if one of my players wants to grapple that grappler. What happens? Does that person take 2 people? 

Grappling a grappler is fine and even the grappled creature can do it. If a nongrappled PC grappled a grappler of an ally and then dragged the grappler away from the ally, this would break the grapple on the ally. 

I hope that is less confusing then it seems.

I agree with Trir, but to go in some detail about why the grapplers grapple would be broken, I would personally say that, in order to contest your grapple, they would need to release their grapple. Otherwise, it would be an auto-success grapple.

Then we get into - what if the grappler doesn't disengage their grapple, not contest your check, and just let themselves be grappled? That... I'm not quite sure how I would go about dealing with that. 

First thought is to make an Athletics (Strength) check to see if you can break the other creature's grapple, made in the same way a grapple action would be done.

Honestly, if the point of this is to break a creature's grapple on an ally, I would just ask to make breaking the grapple my action, then probably do an Athletics (Strength) vs. Athletics (Strength)/Acrobatics (Dexterity) check... again, exactly like a grapple action. Now, I would also allow the grappled ally to use the Help action to give the grappler disadvantage on their roll (as they're really working against the grappler rather than helping their ally break the grapple... it makes sense in my head)

THEN, there's the scenario when a player wants to grapple a creature that is grappling an ally, but the grappler doesn't want to contest the grapple, and the grappler grappling the grappler wants to be able to move both - I would say that the player would need to make an Athletics (Strength) check of... whatever you want it to be, then they can either move quarter speed or not at all (success or failure, respectively.)

But, that's just me. *shrugs*

So here are some of the scenarios.

An Enemy (E) is grappling an Ally (A). A’s speed is 0. E can drag A up to 1/2 E’s speed.

A can attempt to grapple E, if successful, both of their speeds 0.

You can attempt to grapple E. If successful, E’s speed is 0. You can drag E up to 1/2 your speed. If you drag E away from A, E’s grapple on A is broken.

This next scenario is little more questionable.

You can grapple A. A wouldn’t have to oppose your grapple. You can drag A away from E, breaking E’s grapple on A.

Quote from Akacen >>

I agree with Trir, but to go in some detail about why the grapplers grapple would be broken, I would personally say that, in order to contest your grapple, they would need to release their grapple. Otherwise, it would be an auto-success grapple.

Then we get into - what if the grappler doesn't disengage their grapple, not contest your check, and just let themselves be grappled? That... I'm not quite sure how I would go about dealing with that. 

First thought is to make an Athletics (Strength) check to see if you can break the other creature's grapple, made in the same way a grapple action would be done.

Honestly, if the point of this is to break a creature's grapple on an ally, I would just ask to make breaking the grapple my action, then probably do an Athletics (Strength) vs. Athletics (Strength)/Acrobatics (Dexterity) check... again, exactly like a grapple action. Now, I would also allow the grappled ally to use the Help action to give the grappler disadvantage on their roll (as they're really working against the grappler rather than helping their ally break the grapple... it makes sense in my head)

THEN, there's the scenario when a player wants to grapple a creature that is grappling an ally, but the grappler doesn't want to contest the grapple, and the grappler grappling the grappler wants to be able to move both - I would say that the player would need to make an Athletics (Strength) check of... whatever you want it to be, then they can either move quarter speed or not at all (success or failure, respectively.)

But, that's just me. *shrugs*

Bolded part:
I would make them maintain a Con save against a straight strength roll. Think of it as holding your breath to maintain a grapple on someone while someone puts you into a choke hold.

I see a couple of personal rulings mentioned, but this is right according to RAW:

Quote from Trirhabda >>

So here are some of the scenarios.

An Enemy (E) is grappling an Ally (A). A’s speed is 0. E can drag A up to 1/2 E’s speed.

A can attempt to grapple E, if successful, both of their speeds 0.

You can attempt to grapple E. If successful, E’s speed is 0. You can drag E up to 1/2 your speed. If you drag E away from A, E’s grapple on A is broken.

 

This next scenario is little more questionable.

You can grapple A. A wouldn’t have to oppose your grapple. You can drag A away from E, breaking E’s grapple on A.