The most similar game would be RE5 (if you haven't played that) and Dead Space 3.
Weapon customization is a bit more detailed in RE5, where you can upgrade your weapons permanently using cash you obtained from treasures and fallen enemies.
Dead Space 3's weapon customization is much more in-depth, since you're building weapons from scratch and you can get more and more powerful parts as you progress. There's even a "testing room" for you to try out your weapon combinations and check if some parts are compatible with others, like finding out that the electrocution module also works for the circular saw and mines.
Both games have story mode co-op, although in Dead Space 3, you play solo until a second player enters and the storyline changes to accommodate the other character (Carver) being with Isaac all the time. Otherwise, Carver is always separated and is teamed-up with the other NPCs.
I should also point out that RE5's controls are outdated because you can't move while aiming your gun or attacking with the knife. Melee is context-sensitive only, meaning you can only use it when the game tells/lets you.
My thoughts about Bioshock Infinite: http://tinyurl.com/mn5ll4x (WARNING: CONTAINS SPOILERS)