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Learned information and experiences are thought to be stored in synapses, composed of building block molecules whose number typically correlates with synaptic strength. Activity-dependent plasticity mechanisms, such as Hebbian learning, regulate these building blocks, promoting synaptic growth to encode acquired knowledge. However, this process can destabilize cortical networks through overexcitation, leading to runaway dynamics. To prevent such instabilities the brain uses compensatory mechanisms like synaptic scaling. Existing models rely on rapid timescales, contradicting experimental observations that synaptic scaling occurs slowly. Here, we introduce aggregate scaling, a simple framework to study synapse-mediated homeostasis based on the availability and competitive redistribution of synaptic building blocks. Our model enforces stability by integrating rapid regulation of the total synaptic strength and firing rate homeostasis over much slower, realistic timescales. It preserves key neuronal properties, such as firing activity around a homeostatic set-point, long-tailed distributions of synaptic weights, and response to brief stimulation.