Annealing is a valuable method for fine-tuning the ultrasmall magnetic properties of alloy nanoparticles (NPs) by controlling their sizes, modifying their surfaces, and affecting their magnetic interactions. Herein, we study the effect of moderate annealing (450 °C) on strongly interacting NiCr nanoparticle assemblies (0 ≤ atom % Cr ≤ 15) immediately after deposition. Concurrent temperature-dependent electron microscopy and magnetization data demonstrate the interplay of two competing factors, namely, enhanced particle aggregation and element-specific surface segregation, on the magnetic properties, with the former boosting and the latter suppressing them. Strong interparticle interactions can lead to a magnetic response different from that of superparamagnetic particles, namely, from canonical spin-glass (0 atom % Cr) to correlated spin-glass (5-15 atom % Cr) behavior below higher spin-glass transition temperatures Tg (20-350 K). The observation of "high-field susceptibility"below cryogenic temperatures (≤20 K) is ascribed to the presence of inhomogeneity/defects caused by Cr segregation. This work emphasizes the necessity of taking into account the delicate balance of such competing factors to understand the magnetic properties of nanoparticulate samples.