Sweet Business feels lacking in PVE as a primary weapon when it shouldn't, especially since its a bloody chain gun. There are some perks that would really help it out in PVE mostly especially a new perk in the kinetic loot-pool.
Kinetic Tremors: Sustained Kinetic Damage creates a shockwaves on target.
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This would be good for Sweet Business since you can lay on a target in PVE and gain a bonus to damage from the perk while also using it for orange bars in PVE
Target Lock: Increased Damage the Longer You Shoot At A Target
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This would be amazing for Sweet Business in PVE and possibly turn it into a dps option for encounters like Caretaker
Unrelenting: Multi-kills grant health
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Quality of Life for Additional Clear on the Sweet Business
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Those are 3 of my perk selections for the Biz that would help it out in a long run for PVE content, and not be too op in Crucible. There's more exotics than this that could use some new perks to refresh it in everyone's mind and meta list.