The nonlinear stiffened inertial amplifier tuned mass friction damper (NSIATMFD) is introduced in this paper to address the limitations of the conventional tuned mass dampers such as narrow frequency ranges and limited adaptability. In addition, three more novel dampers, such as nonlinear compound stiffened inertial amplifier tuned mass friction dampers (NCSIATMFD), nonlinear nested stiffened inertial amplifier tuned mass friction dampers (NNSIATMFD), and nonlinear levered stiffened inertial amplifier tuned mass friction dampers (NLSIATMFD), are introduced by integrating stiffness and mass amplification mechanisms to increase their vibration reduction capacities. These novel dampers are applied at the top of structures to control their dynamic responses. Newton’s second law is followed to derive the governing equations of motion of the controlled structures. H2 and H optimisation strategies are utilised to derive the exact closed-form expressions for the optimal design parameters of these dampers. The transfer function is developed to derive the frequency domain responses by considering harmonic and random excitations. The frequency domain responses are further validated through numerical studies conducted using the Newmark-beta method and near-field earthquake records. Compared to the conventional tuned mass dampers (TMD), the proposed dampers achieve vibration reduction improvements of 24.24 %, 24.64 %, 23.92 %, and 24.54 %, respectively. The integration of stiffness elements significantly extends the frequency control range, while the frictional damping element enhances energy dissipation capabilities. These results establish the novel designs as effective solutions for dynamic environments, offering robust and adaptive vibration mitigation for structures exposed to diverse excitations, including seismic loads. This research provides a significant advancement in TMD technology for modern engineering applications.