Something I've been pondering... According to the rules of the Attack action, I can stow or equip a weapon every time I make an attack as part of that action.

Attack [Action]

When you take the Attack action, you can make one attack roll with a weapon or an Unarmed Strike.

Equipping and Unequipping Weapons. You can either equip or unequip one weapon when you make an attack as part of this action. You do so either before or after the attack. If you equip a weapon before an attack, you don’t need to use it for that attack. Equipping a weapon includes drawing it from a sheath or picking it up. Unequipping a weapon includes sheathing, stowing, or dropping it.

Moving between Attacks. If you move on your turn and have a feature, such as Extra Attack, that gives you more than one attack as part of the Attack action, you can use some or all of that movement to move between those attacks.

And I still have a free object interaction per turn.
So, with a level 11 Fighter, with Crossbow Expert and 3 attacks per turn, I should be able to do this, assuming I have a Rapier in my main hand, a hand crossbow in my off-hand, and another unequipped hand crossbow in my inventory:

- Make attack #1 with a Rapier equipped.
- As part of attack #1, stow the Rapier after the attack.
- As part of attack #2, equip the hand crossbow from my inventory.
- Make attack #2 with my hand crossbow.
- As a bonus action, make a Light attack with my other hand crossbow.
- Using my free object interaction, stow my main hand crossbow.
- As part of attack #3, equip my Rapier.
- Make attack #3 with my Rapier.

Right?

There’s been a recent debate about this (Balor Vard changing weapons), along with others in the past, so it's something that should be agreed on at your table, depending on how you interpret "Equipping and Unequipping Weapons" (per attack, per Action) and whether "Time-Limited Object Interactions" is in addition to that.

I'd say your scenario is legit, because I think "Equipping and Unequipping Weapons" is once per attack and regarding the free object interaction:

Quote from TarodNet >>

I also think you can equip or unequip a weapon using the "Time-Limited Object Interactions" rule, in addition to the interactions provided by "Equipping and Unequipping Weapons" as part of the Attack action.

An example in the PHB suggests that this is possible:

Russell: I drop my sword and pull out my warhammer [...]

Vulnerability. An attack that deals bludgeoning damage is deadly to skeletons. Shreeve knows this from past experience, which is why she drops her sword and switches to a Bludgeoning weapon. [...]

Also, the SAC says:

Does Crossbow Expert let you fire a Hand Crossbow and then fire it again as a Bonus Action?
The Crossbow Expert feat allows you to fire a Hand Crossbow multiple times on your turn. But you still must abide by the rules of the Hand Crossbow’s Light property, which state that the property’s additional attack must be made with a different weapon.

Can I make an attack with a Light weapon, then draw a second weapon with my other hand and qualify to make the extra attack of the Light property?
Yes. The only requirement for the Light property’s extra attack is that it’s made with a different Light weapon.

EDIT: threads in this subforum, if you feel like revisiting them:

• Weapon swapping and the 2024 PHB 
• Equip or Unequip a weapon - once per attack or once per Attack [Action]? 
• 2024 switching weapons in combat 
• Help Equipping/Unequipping 
• Equipping a weapon when not taking the Attack action eg for True Strike [2024] 
• Free Utilize in 2024? 
• Draw and Stow Weapon 2024 Clarification 
• question about light weapon (dnd2024) 

 And also because the free object interaction...

Interacting with Things. You can interact with one object or feature of the environment for free, during either your move or action. For example, you could open a door during your move as you stride toward a foe.

... has basically the same definition as the Utilize action:

Utilize [Action]

You normally interact with an object while doing something else, such as when you draw a sword as part of the Attack action. When an object requires an action for its use, you take the Utilize action.

And the Utilize action makes it clear that you can also use it to draw weapons as an example.
And finally, there's no mention in here that any resource whatsoever is consumed (not even your free object interaction) when you interact with a weapon and make an attack at the same time:

Equipping and Unequipping Weapons. You can either equip or unequip one weapon when you make an attack as part of this action. You do so either before or after the attack. If you equip a weapon before an attack, you don’t need to use it for that attack. Equipping a weapon includes drawing it from a sheath or picking it up. Unequipping a weapon includes sheathing, stowing, or dropping it.