Little is known about the order of poles of triple tensor product \(L\)-functions in higher rank. In this talk we will investigate the order of the pole of the triple tensor product \(L\)-functions \(L(s,\pi_1\times\pi_2\times\pi_3,\otimes^3)\) for cuspidal automorphic representations \(\pi_i\) of \(\GL_{n_i}(\A_F)\) in the setting where one of the \(\pi_i\) is a monomial representation. In the view of Brauer theory, this is a natural setting to consider. The results provided in this talk give examples that can be used as a point of reference for Langlands’ beyond endoscopy proposal.