You can use the EXP+ items or use other Cosmoloids as catalyst in augmentation to boost and level up Cosmoloid of your choice.

So far C grade standard Cosmoloid will grant 1000 exp, their equipped parts will not be destroyed. (Need info and confirmation on other grade levels)

Know augmentation items:

EXP+100, EXP+300, EXP+500, EXP+1000