Let $\Phi$ be a finite root system. A $\Phi$-graded group is a group $G$ together with a family of subgroups $(U\alpha)$ $\alpha \in \Phi$ satisfying some purely combinatorial axioms. The main examples of such groups are the Chevalley groups of type $\Phi$, which are defined over commutative rings and which satisfy the well-known Chevalley commutator formula. We show that if $\Phi$ is of rank at least 3, then every $\Phi$-graded group is defined over some algebraic structure (e.g. a ring, possibly non-commutative or, in low ranks, even non-associative) such that a generalised version of the Chevalley commutator formula is satisfied. A new computational method called the blueprint technique is crucial in overcoming certain problems in characteristic 2. This method is inspired by a paper of Ronan-Tits.