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.