  We study inverse boundary problems for third-order nonlinear tensorial
perturbations of biharmonic operators on a bounded domain in $\mathbb{R}^n$,
where $n\geq 3$. By imposing appropriate assumptions on the nonlinearity, we
demonstrate that the Dirichlet-to-Neumann map, known on the boundary of the
domain, uniquely determines the genuinely nonlinear tensorial third-order
perturbations of the biharmonic operator. The proof relies on the inversion of
certain generalized momentum ray transforms on symmetric tensor fields.
Notably, the corresponding inverse boundary problem for linear tensorial
third-order perturbations of the biharmonic operator remains an open question.
