Are you allowed to draw/switch weapons between attacks?

The main reason Im asking is for considering thrown melee weapons. If a fighter has three attacks they can make and also has three javelins, are they allowed to throw a javelin, draw another, throw it, and so on? I'm inclined to say they can, but I am not 100% sure.

You can draw or stow 1 weapon for free on each of your turns as part of the free item interaction. In order to draw additional weapons you will need a feat, fighting style, or to use the [Tooltip Not Found] action.

The Thrown fighting style specifically addresses the fact that Thrown weapons don't play nicely with the one free weapon draw. If you're planning to throw Javelins and have even as few as two attacks per round, it's pretty necessary. Depending on how your DM interprets Dual Wielder (two free weapons draws per round? Or just can draw two at once with your one free weapon draw?), that might do some mileage too.

Thrown Weapon Fighting
You can draw a weapon that has the thrown property as part of the attack you make with the weapon.
In addition, when you hit with a ranged attack using a thrown weapon, you gain a +2 bonus to the damage roll.

Thanks for the responses. It makes more sense now. I was really unsure of how drawing weapons on a combat turned worked and usually just allow them as free actions anyway, but usually my party would only be drawing one or two weapons on a given turn, so it wasn't an issue until now. 

My reading of the Extra Attack and Multiple Attack features is that the only thing you can do betwen the attacks is move.

You explicitly can draw weapons as part of "an attack," so I'd hope that you would recognize that at least as being something you can do between separate attacks and not just with the first attack of an attack action. 

You normally interact with an object while doing something else, such as when you draw a sword as part of an attack.

The sidebar (found on dndbeyond below the "being prone" section) also lists a great number of free interactions that can be done "in tandem with your movement and action" in general, which I would hope you would also recognize can be done at any point during the Attack Action and not just at the start. I suppose you could disagree and read "in tandem" as "in addition" and not "at the same time as," but that isn't really what "in tandem" means (alongside; together).

Beyond that though, most people play that other things like a Bonus Action Two-Weapon Fighting attack can sandwich in between multiple Attack Action attacks. It's "when you take...," not "after you take" after all:

Two-Weapon Fighting

When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand. 

The Bonus Actions section in general includes some very permissive timing language, stating that "you choose when to take a bonus action during your turn", unless the bonus action itself specifies a time restriction. Nothing in Attack, or any other Action, says specifically that it must be finished to completion without interruption, and nothing in Bonus Actions specifically directs you not to sandwich it mid-Action, so I don't see a RAW support for requiring an Attack Action to be completed with no interruption. Attack Action attack 1, Bonus Action-Disengage (from Cunning Action), move, Attack Action attack 2 is a pretty common scenario, with no text that I can find telling you it would be prohibited.