Catscratch | "True Melee"/Pet Vex

Weapons
You ideally want a gun in each of the primary elements for mobbing.
For when you need to shoot, you want a gun with either multiple projectiles or fast fire rate for the Cursed Blade damage proc. Shotguns tend to work best for this.

• Be wary, certain guns have slower melee attack animations. Hadn't worked out which ones or why but please be cautious about it if you feel your melee looking slow to reset between swings.
• To my knowledge, guns that have bladed parts on them do NOT boost melee damage. The animation will look different and cool, and may even have a lower reset time, but it does not boost damage.
  

Shield
Synergy between Teen Witch and Heavyweight allow us to constantly keep re-proccing the extra melee damage effect and maintain our specialization boosts as long as we can keep Overshield active.
A weird quick with this synergy include "breaking" when your shield is at partial intervals and you try to melee. I'm not quite sure if this is a sort of internal cooldown or just a byproduct of how shield steal works.

Missile Swarm and Mini-Nova are two both fantastic options to have.

• Mini-Nova works great with mobbing for the extra elemental damage to help shred through Shield bars. This also makes the build feel like you're using the Love Thumper from BL2.
• Missile Swarm works wonderful on bossing, especially when combined with the Slippy. Some extra tech with the Missile Swarm is that it counts as gun damage, which means it stacks Recurrence. They also proc the Cursed Blade damage and benefit from Infusion.

Class Mod
Because this build relies on constantly refilling Heavyweight, our COM Slot is very locked to the Teen Witch legendary class mod.
I prefer having as many points in Corporeal as possible for the better Overshield max capacity but also the damage bonus.
Good passive rolls include Melee Damage, Melee Crit Chance, and All Damage Dealt.
Both Melee and Melee Crit chance apply to Trouble. Melee Crit chance is funnier.

Ordnance
The Slippy is our get out of jail free card for flying enemies and bulky bulkheads.
It is also our prime way to stack Groundbreaker against large bosses. With a good throw, you can get many Slippy procs in a short amount of time and then unleash a huge Groundbreaker punch/slam.
Works great against larger flying bosses and Vile Kratches since the Slippy can get stuck in their big stupid hitboxes.
A cool bit of tech is that Vex's Phase Covenant converts Slippy's element to the element of your current attunement.

Repkit
Triple Bypass has the best spammability for our needs of proccing Infusion for our's and Trouble's melee hits.
For rolls, use one with Heavy Hitter for melee damage, but you can also use Enrage for soup or Accelerator for more CDR.

Enhancement
No Enhancements provide any practical bonus for melee damage.
Gun Equip speed is still extremely useful to have and should be the main passive you're looking out for. You are able to get generic and specific gun-type equip speed on the same COM.

Action Fist works best to fully lean into that hybrid playstyle between you and Trouble. At 3/3, your melee kills will buff Trouble's damage.
Reel Big Fist is the only other one that interests me because of the high amount of melee damage.

The choice between your 3/3 bonus is whether you want the Consistent Trouble damage or you want the Bloodsplosion-like chaining novas from Melee kills with Reel Big Fist (of which Trouble can also proc too).

Airstrike can also be used alongside 3/3 Reel Big Fist and Mini-Nova Heavyweight to give all of those novas a much larger splash radius. Since we can't really benefit from either 3/3 effect in bossing, this also becomes helpful for consistency for Slippy damage and Groundbreaker slams.

With the Groundbreaker change to not recursively loop into itself, we can reliably use this specialization for bossing. Refer to the bossing setup down below.

The Best Defense is really good all general damage.

Now With Caffeine with Triple Bypass is a great way to passively lower our cooldown in chunks. We do not fully rely on this for Cooldown but it can be helpful for extended mobbing. With this in mind, you still want to pace out your Triple Bypasses for Infusion moreso Cooldown.

A Honed Mind is a nice little boost of damage for Trouble. With Crit Chance COM and Vorpal Fang it works out to be around 25% crit chance for Trouble which is delightful to have.