This paper investigates the response attenuation of a hardening Düffing oscillator utilizing a Nonlinear Tuned Mass Damper (NTMD), a Semi-Active Tuned Mass Damper (STMD), and a multiple TMD (MTMD) consisting of the two in parallel. A high amplitude “detached” solution branch in the frequency-response of the primary structure is observed in the case of an NTMD. By adding an STMD to the NTMD in parallel, the study indicates that the high amplitude detached resonance can be significantly attenuated. The MTMD (NTMD+STMD) is found effective in suppressing both the steady-state and transient responses. A parametric study of the design parameters of the MTMD is conducted. It is found that the addition of an STMD with a small mass ratio and small damping ratio in parallel with an NTMD results in significant reduction of steady-state response. For transient response reduction, the study shows that the damping ratio of NTMD has a significant effect while the other parameters have minimal effects. Increasing the damping ratio of the NTMD (up to a critical value) increases the decay rate of the transient responses. These results indicate that the design parameters for the MTMD should be appropriately selected to ensure that the MTMD attenuates both the steady-state and transient response effectively.