Pick a class that has access to the Extra Attack feature. For my example, I'll use my standby, Fighter McFighterson.
Let us say that McFighterson is 20th level, and possesses the Dual Wielder feat. He is currently holding a greatsword, and has two longswords accessible.
As a reminder, two weapon fighting says:
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…[snip]
And Dual Wielder:
[snip]… You can use two-weapon fighting even when the one handed melee weapons you are wielding aren’t light.
You can draw or stow two one-handed weapons when you would normally be able to draw or stow only one. …[snip]
Can McFighterson make all of the attacks granted by Extra Attack (3, in this case) with his greatsword, drop the greatsword "for free", draw two longswords (as permitted by Dual Wielder), use his last attack to attack with one longsword, then two-weapon-fight with the second longsword?
Making the attack sequence look something like:
Greatsword, Greatsword, Greatsword, Longsword1, Longsword2.
Related: Does Two-Weapon fighting work if you aren't holding both weapons when you take Attack action?
Best Answer
Yes, you may.
There is no limitation built into the Two-Weapon Fighting rule to deny that. It only requires taking the Attack action, and making at least one melee attack with a one-handed weapon.
Dropping the greatsword doesn't cost an action, drawing a weapon is considered interacting with an object, and drawing a second weapon is included in the object interaction thanks to the Dual Wielder feat. The PHB even specifies that drawing a weapon can be done in the middle of an action or movement, so drawing a weapon between extra attacks is permissible.
As part of your Attack action, you have attacked with a one handed weapon, which means you can use your bonus action for an off-handed attack.