The 0(3P) + C2H4 reaction provides a crucial, initial understanding of hydrocarbon combustion. In this work, the lowest-lying triplet potential energy surface is extensively explored at the multiconfiguration self-consistent field (MCSCF) and MRMP2 levels with a preliminary surface crossing investigation; and in cases that additional dynamical correlation is necessary, MR-AQCC stationary points are also determined. In particular, a careful determination of the active space along the intrinsic reaction pathway is necessary; and in some cases, more than one active space must be explored for computational feasibility. The resulting triplet potential energy surface geometries mostly agree with geometries from methods using single determinant references. However, although the selected multireference methods lead to energetics that agree well, only qualitative agreement was found with the energetics from the single determinant reference methods. Challenges and areas of further exploration are discussed.