Biomolecular condensates enable spatial and temporal control over cellular processes by concentrating biomolecules into nonstoichiometric assemblies. Many condensates form via reversible phase transitions of condensate-specific multivalent macromolecules known as scaffolds. Phase transitions of scaffolds can be regulated by changing the concentrations of ligands, which are defined as nonscaffold molecules that bind to specific sites on scaffolds. Here, we use theory and computation to uncover rules that underlie ligand-mediated control over scaffold phase behavior. We use the stickers-and-spacers model wherein reversible noncovalent cross-links among stickers drive phase transitions of scaffolds, and spacers modulate the driving forces for phase transitions. We find that the modulatory effects of ligands are governed by the valence of ligands, whether they bind directly to stickers versus spacers, and the relative affinities of ligand–scaffold versus scaffold–scaffold interactions. In general, all ligands have a diluting effect on the concentration of scaffolds within condensates. Whereas monovalent ligands destabilize condensates, multivalent ligands can stabilize condensates by binding directly to spacers or destabilize condensates by binding directly to stickers. Bipartite ligands that bind to stickers and spacers can alter the structural organization of scaffold molecules within condensates even when they have a null effect on condensate stability. Our work highlights the importance of measuring dilute phase concentrations of scaffolds as a function of ligand concentration in cells. This can reveal whether ligands modulate scaffold phase behavior by enabling or suppressing phase separation at endogenous levels, thereby regulating the formation and dissolution of condensates in vivo.