Fiedler vector, what else?

Yes. See e.g. the paper Multi-way spectral partitioning and higher-order Cheeger inequalities by Lee, Oveis-Gharan and Trevisan. They show how the first $k$ eigenvectors can be used to find a useful $k$-way partitioning.

The Fiedler vector refers to the second smallest eigenvalue, here is a study of The third smallest eigenvalue of the Laplacian matrix (2001).

The relationship between the third smallest eigenvalue of the Laplacian matrix and the graph structure is explored. For a tree the complete description of the eigenvector corresponding to this eigenvalue is given and some results about the multiplicity of this eigenvalue are given.