Increase your utility perks from levels 11 to 20, like Scrounger, Locksmith, and Hacker. Moreover, take Science at 19 because, with Gun Nut and Armorer, you should gain access to better weapon and armor mods. Don’t spend more points on Hacker or Locksmith beyond level 3 because it doesn’t influence the doors you can open.
Here’s a list of the best perks to select from levels 11 to 20 with the Brotherhood of Steel Build Guide in Fallout 4:
Level 11 – Scrounger 2
Level 12 – Locksmith 2
Level 13 – Hacker 2
Level 14 – Nuclear Physicist 2
Level 15 – Heavy Gunner 2
Level 16 – Armorer 2
Level 17 – Gun Nut 2
Level 18 – Locksmith 3
Level 19 – Science
Level 20 – Save