It has already been shown here that the booming blade cantrip and the Spell Sniper feat do work together, and here that the Sorcerer's Distant Spell Metamagic option and Spell Sniper also stack.
I am wondering if there is any reason the following build does not work:
Alice is a Bugbear multiclassed Sorcerer/Fighter (Battle Master) with the Spell Sniper feat, and she casts booming blade.
The range of booming blade is usually 5 feet. However, she has Spell Sniper which doubles the range to 10 feet, and she uses Distant Spell, which doubles the range again, to 20 feet.
She is holding a reach weapon, which has a reach of 10 feet. And she uses the Battle Master maneuver Lunging Attack, which increases the reach to 15. She then benefits from the Bugbear's Long-Limbed Feature, which increases the reach to 20.
Thus booming blade has a range of 20 feet and Alice has a reach of 20 feet, and so she can use booming blade from 20 feet away.
Is this correct? Have I correctly interpreted how these features work together to allow booming blade to work from 20 feet away?