This work presents the results of a multi-mode iter study on toroidal Alfvén eigenmodes (TAEs), using the nonlinear hybrid Hagis-Ligka model. It is found that main conclusions from earlier studies of Asdex Upgrade discharges can be transferred to the iter scenario: global, nonlinear effects are crucial for the evolution of the multi-mode scenario. This work focuses on the iter 15 MA baseline scenario with a safety factor at the magnetic axis of q0 = 0.986. The least damped eigenmodes of the system are identified with the gyrokinetic, non-perturbative Ligka solver, concerning the mode structure, frequency and damping. Taking into account all weakly damped modes that can be identified linearly, nonlinear simulations with Hagis reveal strong multi-mode behaviour: while in some parameter ranges, quasilinear estimates turn out to be reasonable approximations for the nonlinearly relaxed energetic particle (EP) profile, under certain conditions low-n TAE branches can be excited. As a consequence, not only grow amplitudes of all modes to (up to orders of magnitude) higher values compared to the single mode cases but also, strong redistribution is triggered in the outer radial area between and 0.85, far above quasilinear estimates.