To advance, to progress.
A synonym for 'go to the next level' is advance.
The word "adjacent" means next to or adjoining something.
A six letter word that also means next to is beside
Next means being nearest to, first ensuing or immediately following
Ground level
Elevation is the word that means the height of land above sea level.
Heir
subsequent
The root word 'grad' means step. For instance gradual means progress little by little. Graduate means step up to the next level.
adjacent means next to, so i will say another word is NEXT TO
elavate
level