A global model perturbed parameter ensemble of 60 simulations was used to explore how combinations of six parameters related to secondary organic aerosol (SOA) formation affect particle number concentrations and organic aerosol mass. The parameters represent the formation of organic compounds with different volatilities from biogenic and anthropogenic sources. The most plausible parameter combinations were determined by comparing the simulations against observations of the number concentration of particles larger than 3 nm diameter (N3), the number concentration of particles larger than 50 nm diameter (N50), and the organic aerosol (OA) mass concentration. The simulations expose a high degree of model equifinality in which the skill of widely different parameter combinations cannot be distinguished against observations. We therefore conclude that, based on the observations we have used, a six-parameter SOA scheme is under-determined. Nevertheless, the model skill in simulating N3 and N50 is clearly determined by the low-volatility and extremely low-volatility compounds that affect new particle formation and growth, and the skill in simulating OA mass is determined by the low-volatility and semi-volatile compounds. The biogenic low-volatility class of compounds that grow nucleated clusters and condense on all particles is found to have the strongest effect on the model skill in simulating N3, N50, and OA. The simulations also expose potential structural deficiencies in the model: we find that parameter combinations that are best for N3 and N50 are worst for OA mass, and the ensemble exaggerates the observed seasonal cycle of particle concentrations - a deficiency that we conclude requires an additional anthropogenic source of either primary or secondary particles.