From levels 31 to 40, you want increased damage and damage reduction. At level 30 and beyond, you will start encountering more difficulty enemies and bosses. Moreover, increasing crafting through Gun Nut and Armor can also aid in damage and damage reduction through upgrades.
Here’s a list of Perks to select from levels 31 to 40 with the Best Shotgun Build Guide in Fallout 4:
Level 31 – Rifleman 4 + Bloody Mess 3
Level 32 – Demolition Expert 2
Level 33 – Medic 2
Level 34 – Toughness 2
Level 35 – Life Giver 2
Level 36 – Adamantium Skeleton
Level 37 – Chemist
Level 38 – Save
Level 39 – Gun Nut 4 + Armorer 4
Level 40 – Lone Wanderer 3