You can use pretty much any secondary and melee you want.
Health Conversion is used over Adaptation since a) you already have 90% from your 2 and b) it gives you Companion a shit ton of armor for just as much DR. Same reason for Blessing: we want our companion to stay alive. If you're in a shorter mission, swap out Augmented with Impetus. I also suggest subsuming Roar over her 4. Shards are also a Tau Violet for Equilibrium Effect, a Tau Yellow for Cast Speed, and three Red Taus for Strength (or duration, but I don't think you get enough to be worth it).

Primary is going to be the Paris Prime with all the status mods and some crit chance to give our companion 374% status chance and 83% crit chance. Arcane can be anything but Dexterity is fine. Unranked Hunter Track is purely for the special effect since it'll be free damage.

Medjay is where all the magic happens.
This video explains the insane synergy between the first three mods, but the short version is that the first two mods work with Contagious Bond to give maximum status spread. Viscous Bond is perfect here since we're always casting our 1 to tag mobs. Duplex Bond is very important as while the true companion only gets the effect, the amount of beams increases with the amount of companions. Momentous Bond is more for free damage than reviving but Tenacious Bond is also an option. Than Link Mods for insane EHP.

For Posture, Assassin is basically the go-to given how Magnetic procs turn into Electric Damage. Everything else is pretty standard. You might be wondering why Shock instead of Burning, and that's because of Heat Inherit stuff and beams proccing it before companions.

I think that should be everything.