Singlet fission (SF) is a process where a singlet exciton is split into a pair of triplet excitons. The increase in the excitonic generation can be exploited to enhance the efficiency of solar cells. Molecules with conjugated π bonds are commonly developed for optoelectronic applications including SF, due to their low energy gaps. The electronic coupling for SF in such well-stacked π-conjugated molecule pairs can be rather limited due to the orthogonal π and π* orbital overlaps that are involved in the coupling elements, leading to a large cancellation in the coupling. In the present work, we show that such limits can be removed by involving triplet states of different origins, such as those with nonbonding n orbitals. We demonstrate such an effect for formaldehyde and methylenimine dimers, with a low-lying n-π* triplet state (T1) in addition to the π-π* triplet (T2). We show that the coupling can be enhanced by 40 times or more for the formaldehyde dimer, and 15 times or more for the methylenimine dimer, with the T1-T2 state as the end product of SF. With 1759 randomly oriented pairs of formaldehyde derived from a molecular dynamics simulation, the coupling from a singlet exciton to this T1-T2 state is, on an average, almost two times larger than that for a regular T1-T1 state. We investigated a few families that have been shown to be prospective candidates for SF, using our proposed strategy. However, our unfavorable results indicate that there are clear difficulties in fulfilling the ES1 ≳ ET1 + ET2 energy criterion. Nevertheless, our results provide a new molecular design concept for better SF (and triplet-triplet annihilation, TTA) materials that allows future development.