I think I understand how to define the algebraic fundamental group $\pi^{alg}_{1}(X)$ of a scheme and I think I understand the relation between $\pi^{alg}_{1}(X)$ and $\pi_{1}(X(\mathbb{C}))$, where $X$ is a nice algebraic variety over complex numbers $\mathbb{C}$.

Is it reasonable to hope for a definition of higher algebraic homotopy groups $\pi_{n}^{alg}(X)$ of a scheme $X$ ?