My paper with Liang Kong, arXiv:1405.5858, presents the following conjecture:
Bosonic topological orders in $n$-space-time dimensions (after quotient out the invertible topological orders) are described/classified by modular unitary $n$-categories with one object.
The reason that modular unitary $n$-categories fail to classify topological orders is because modular unitary $n$-categories with one object describe/classify topological excitations. The invertible topological orders has no non-trivial topological excitations. Thus all invertible topological orders correspond to the same trivial unitary $n$-category with one object. But after we quotient out the invertible topological orders, modular unitary $n$-categories with one object classify bosonic topological orders in $n$-space-time dimensions.