To enhance the transmission capacity of fiber-to-the-home（FTTH）systems and address the limitations of traditional triplexers in polarization dependency and multiplexing capability, a silicon nitride（SiN）multimode interference-based triplexer supporting multi-dimensional multiplexing integration was designed. This device employs a Bragg grating-assisted tilted multimode interference coupler structure. By optimizing the width and position of the input/output waveguides, the tilt angle, and the parameters of the segmented gratings, multiplexing and demultiplexing of eighteen channels are achieved, corresponds to three wavelengths（1 310 nm, 1 490 nm, 1 550 nm）, dual polarization states, and third-order modes. The simulation results show that the insertion loss of each channel is below 1.05 dB, the crosstalk is better than -12.5 dB, and excellent temperature stability and process tolerance are achieved. The temperature drift rates for the transverse electric（TE）and transverse magnetic（TM）modes are as low as 17 pm/°C and 27 pm/°C, respectively.