We explore via spectroscopic modeling whether the highly correlated diffuse interstellar bands at 6613.6 and 6196.0 Å might originate from a single molecule. Efforts were made to simulate the band contours of the DIBs along the three lines-of-sight, which have been observed by others at high resolution: HD179406, HD174165, and Her 36. Reasonable simultaneous fits were obtained using a prolate symmetric top molecule that exhibits transitions of two different band types, type-a parallel and type-b perpendicular bands. Two different excited states of a long-or heavy-chain, forked molecule are proposed. A minimum number of adjustable parameters were used including ground and excited state A and B rotational constants, an excited state centrifugal distortion constant, and three different rotational excitation temperatures. Points in favor and against the hypothesis are discussed.