The growth of freshly formed aerosol particles can be the bottleneck in their survival to cloud condensation nuclei. It is therefore crucial to understand how particles grow in the atmosphere. Insufficient experimental data has impeded a profound understanding of nano-particle growth under atmospheric conditions. Here we study nano-particle growth in the CLOUD (Cosmics Leaving OUtdoors Droplets) chamber, starting from the formation of molecular clusters. We present measured growth rates at sub-3 nm sizes with different atmospherically relevant concentrations of sulphuric acid, water, ammonia and dimethylamine. We find that atmospheric ions and small acid-base clusters, which are not generally accounted for in the measurement of sulphuric acid vapour, can participate in the growth process, leading to enhanced growth rates. The availability of compounds capable of stabilizing sulphuric acid clusters governs the magnitude of these effects and thus the exact growth mechanism. We bring these observations into a coherent framework and discuss their significance in the atmosphere.