The penalty is being in difficult terrain

You're in difficult terrain for all creatures occupying the same space:

The space of another creature, whether hostile or not, also counts as difficult terrain.

The constraint is that creatures in the situation must attempt to move out of it.

The rules have a provision that generally avoids the stacking situation:

Whether a creature is a friend or an enemy, you can't willingly end your move in its space.

Grappling an unwilling ally will arrest them in your square: a clever edge case.

You can grapple your ally, providing they're unwilling, as grapple is a contest[1,2]. Sometimes one has to hold back their friend. The no-contest version is not a grapple, but is covered under the drag/lift/carry rules.

Cleverly grappling your ally to arrest their motion will work for a round. On the next round, both the grappler and the grappled characters must to attempt to move out of the square as long as they're both occupying it. Not attempting to move out of the square would mean they're willingly ending their move there, and that's not permitted per the rule cited above.

This is an example of the edge case of the rules and can be further manipulated into a broken situation that ends with a DM narrating when it stops.

The rules do not state a limit of the number of creatures in a space, because 5e rules are not a physics engine.

There are currently not specific rules about the number of creatures that can occupy a space. The provision is that they can't willingly do so in combat.

Making a large stack of creatures is similar to such endeavors as a peasant railgun or a hired army running through a teleportation circle.

Whether a creature is a friend or an enemy, you can’t willingly end your move in its space.

Emphasis mine.

Consider You and another creature (Zorb). If you are forced to share a space with Zorb, it happens - no shunting in any directions unless something specifically tells you to.
So, if you fail a save against polymorph and are turned into a Large creature (and your new size overlaps with Zorb's space), then you are sharing a space with Zorb.
On your next turn (or Zorb's next turn, if it happens first), you must move to no longer be sharing a space (if it's possible).

That's RAW.

As far as how I would adjucate it: I would make use of the Squeezing rules.

Squeezing into a Smaller Space
A creature can squeeze through a space that is large enough for a creature one size smaller than it. Thus, a Large creature can squeeze through a passage that’s only 5 feet wide. While squeezing through a space, a creature must spend 1 extra foot for every foot it moves there, and it has disadvantage on attack rolls and Dexterity saving throws. Attack rolls against the creature have advantage while it’s in the smaller space

(thanks KorvinStarmast for the rules text)

I would mandate that you Squeeze so that your Large form only occupies a Medium creature's space (and no overlap happens in the first place), and that you cannot stop Squeezing until there is room for your entire form.

But that is not RAW, and is merely my opinion.