In this paper, an asymmetric plasmonic structure composed of two MIM (metal-insulator-metal) waveguides and two rectangular cavities is reported, which can support triple Fano resonances originating from three different mechanisms. And the multimode interference coupled mode theory (MICMT) including coupling phases is proposed based on single mode coupled mode theory (CMT), which is used for describing and explaining the multiple Fano resonance phenomenon in coupled plasmonic resonator systems. Just because the triple Fano resonances originate from three different mechanisms, each Fano resonance can be tuned independently or semi-independently by changing the parameters of the two rectangular cavities. Such, a narrow 'M' type of double Lorentzian-like line-shape transmission windows with the position and the full width at half maximum (FWHM) can be tuned freely is constructed by changing the parameters of the two cavities appropriately, which can find widely applications in sensors, nonlinear and slow-light devices.