This paper investigates how targeted interference between two well characterized sources of hydrodynamic disturbances can modify the response of premixed bluff body stabilised H 2 / CH 4 flames with and without swirl. We introduce modulations into the Flame Transfer Function (FTF) through hydrodynamic interference between the shedding of vortices/wakes from different shaped bodies upstream of the flame and the vortex roll-up at the flame base caused by acoustic forcing. By placing a set of small diameter cylinders, a streamlined body, or a swirler upstream of the bluff body and varying the distance from the dump plane, the gain and phase of the FTFs could be modulated at targeted frequencies providing a method to suppress thermoacoustic instabilities. We further investigate the flame response which shows that modulations in the fluctuating global heat release rate are caused by linear superposition along the flame front. At frequencies leading to destructive interference, large-scale wrinkling of the flame front occurs which increases the flame surface area but is offset by the simultaneous pinch-off of the flame tip which decreases flame surface area. Their combined effect reduces the amplitude of the fluctuating global heat release rate. At frequencies of constructive interference, large-scale wrinkling of the flame occurs before the flame tip pinches off, leading to an overall increase in the flame surface and amplitude of the fluctuating global heat release rate.