It was recently pointed out to me that, for combat purposes, since 2 medium creatures, or a medium and a small creature, cannot occupy the same 5' space when your turn ends, and that even if the rules were bent to allow for the squeezing rule, both players would fight at disadvantage. I never considered  this, and I can find no one commenting on this, but would this mean then that only 1 creature is meant to use a broom of flying at time, not multiple as I have always been allowing?

To make sure I understand you, are you saying that more than one creature is able to occupy the same 5' square at the end of their turn?

As always the DM has final say. I would not allow two creatures on the same broom during combat unless they were both small and one was simply a pilot. (As in two goblin brothers cackling maniacally while one pilots and the other flings projectiles.) Two medium sized creatures would probably exceed the broom's weight limit anyways, but that would just reduce the speed from 50' to 30'. 

RAW (and according to Jeremy Crawford RAI) you can't willingly end your move in another creature's space. You can move through the space of a friendly creature as difficult terrain. You can move through a hostile creature if it is two sizes larger than you as difficult terrain. (With a halfling being able to move through a hostile medium creature's space as well.) Meaning you can move through then attack but you can't move into the space, attack, and then continue to move. 

There is no rule that specifically states what happens when two creatures start their turn in the same space. After all, when you grapple someone you're not holding them five feet away from you. And if a creature is one size larger than you then you can use them as a mount, and thus are always in their same space until you dismount. 

Regardless of what the rules do or do not say, it's your game. If you and your players have been happy with the tandem broom then don't change anything. In the real world we have bicycles built for two so why wouldn't there be brooms of flying built for two? Artificers have romantic feelings just like everyone else. 

The rules they cited above are pretty clear that two creatures can not occupy  the same 5' square.

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

So if there are two creatures riding on a broom in combat then when they take their turns, the first one will have to hop off the broom since they can't willingly end their turn in the same space as another creature. So, RAW, things would appear to be limited.

However, it is important to keep in mind that the Moving around other creatures rules apply to combat specifically. Out of combat, it is up to the DM how many creatures can fit on the head of a pin. A DM could allow 20 creatures to pile into a carriage for example but if the situation changes and the creatures want to start fighting then, RAW, they need to all get out of the carriage since they can't willingly remain in the space occupied by another creature.

Last comment :) ... it is ultimately up to your DM to decide how they want to run it so ask them. A DM might allow two small creatures to fight from a broom depending on what they are doing ... waving hands and casting spells might be ok ... both wielding bows and trying to shoot might not. The easiest decision would just be to say that the two creatures can't fight effectively from a broom and one needs to hop off. On the other hand, the DM is likely to allow as many creatures as can hold on up to the weight limit to ride on the broom to be moved from one location to anther.

The rules for Moving Around Other Creatures are taken from the Combat chapter. In other circumstances creature can easily move and get closer, even go on top of each other  ;) 

Another noteworthy rule is creature size, which explain that the creature's space is the area it controls in combat, not its dimensions. So when not in combat, the only question that matters is if the creatures weight more than 400 pounds and if the broom is big enought to take place on it.

Creature Size: Each creature takes up a different amount of space. A creature's space is the area in feet that it effectively controls in combat, not an expression of its physical dimensions. A typical Medium creature isn't 5 feet wide, for example, but it does control a space that wide.

Standard sized broom? Comfortably? Two Medium sized or four small sized humanoids. Think about it less from a mechanic rule perspective and just imagine it. You couldn't really fit more than two humans on a regular broom, right? Same logic should apply to the game.

Well listen, if you have one sitting on the broom and one hanging from the broom, the characters could totally occupy two different squares. So, in my opinion, you're totally fine in your ruling. 😜

I'd rule one person per broom, BUT, one person can, theoretically and with a little difficulty (meaning disadvantage for the attacker), hold a second person who can attack.

So person A rides the broom and does not attack. They are focused on holding (voluntary restraint??? ) Person B and flying and that's way more than a person should be doing even remotely safely.

Person B is being held, but gets to experience a bit of a bumpy ridge with a "distracted driver" of sorts. They can take an attack, but it will be with disadvantage (or if it's a spell and the creature needs to make a saving through, the monster gets advantage, which my way of giving disadvantage to the caster).

Quote from Brian_Avery >>

If we adhere to the rule that you cannot end your movement within the same 5' space then how can anyone ever ride a mount? Wouldn't they have to hop off at the end of their turn?

We often see in westerns and fantasy movies how someone not only rides a horse without jumping off every 6 seconds but they sometimes reach down with one arm and help scoop someone else up onto the back of the horse and they both ride off.

 Two things here: first of all, Mount rules are specific rules that override the normal rules about sharing space. This kind of thing happens all over D&D, it's not a contradiction at all. In most cases, those same rules dictate that the mount is quite restricted in what it can do while mounted.

Second of all, a creature needs to be larger than you to be a mount, and as in your "Western" example, horses are large. A broom is not. Two creatures fitting on a large mount is reasonable, although I'd argue they would get in each other's way while trying to fight.

Lastly, the Broom of Flying is already at the top of every list of magic items that are overpowered for their tier. Restricting it to one character helps to limit this imbalance. If you want a magic item that can carry more than one creature in the air, that's what the magic carpet was designed for - and notice it has a higher rarity.

Judging by how the Broom of Flying keeps refering to "you" when standing astride it then hovers beneath you to be ridden in the air until you land makes me think it was intended for solo use regardless of size or weight though.  It will be my ruling in the campaign i'm running right now as there will be one as treasure.

I have always (going back to 1980 or so) ruled that a broom of flying carries one.

That's me, though. I also use mounted rules for them, so yes, the swoop and save someone thing is fine.

A magic carpet depends on the size of it, but is the usual "two or more" vehicle of that sort.

Again, that is me. I will not say you are right or wrong, because I could totally decide in my next world that two people can ride a broomstick.

In short, how you decide it, no matter what that is, has my backing.

I would stay away from Mount rules on objects since they're designed for creatures.

Quote from Plaguescarred >>

I would stay away from Mount rules on objects since they're designed for creatures.

 
except that vehicles rules *are* mount rules, and not all vehicles are creatures.

Quote from AEDorsay >> 

except that vehicles rules *are* mount rules, and not all vehicles are creatures.

There are differences. For example a creature mount can take the dash action and (unless it is independent) only move just before or just after your turn. (Independent mounts retain their own initiative order and have all their abilities.) You can't (RAW) dash on a broom of flying. But the broom can be commanded to travel up to one mile away (to a location you're familiar with) and then commanded to return (if you are still within one mile of it). A creature mount can't do that. And the broom is not a vehicle, it is a magic object. 

As far as vehicles, wagons and ships are vehicles and mount rules do not apply to them. 

Vehicles generally have their own rules and abilities. 

Quote from AEDorsay >>

Quote from Plaguescarred >>

I would stay away from Mount rules on objects since they're designed for creatures.

 
except that vehicles rules *are* mount rules, and not all vehicles are creatures.

 Mount and vehicle are two different things operating under their own specific rules.