Mufflers with multiple inlets and multiple outlets are commonly used in exhaust systems which provide the benefits of lower restriction and higher engine performance. In this paper, the direct mixed-body boundary element method (BEM) is used to predict the transmission loss (TL) of mufflers with two inlets and one or two outlets. To do this, the impedance matrix of the muffler is first computed by the BEM. The transmission loss (TL) can then be evaluated from the impedance matrix which relates the sound pressure at the inlets and the outlets to their corresponding normal particle velocities. A complex-number ratio of the incident sound pressure at the second inlet to the incident sound pressure at the first inlet will need to be supplied before the TL can be evaluated. Numerical test cases are given in the paper, and results are verified by comparing to the five-point method and the six-point method. It is also shown in this paper that the five-point and six-point methods can not be used alone as a TL computational tool because both rely on a ratio derived from the impedance matrix.