Biomolecular condensates are thought to form via phase transitions of multivalent macromolecules. Components of condensates have been classified as scaffolds and clients. In this classification, scaffolds drive condensate formation whereas clients partition into condensates. However, non-scaffold molecules can be ligands that modulate the phase behavior of scaffolds via preferential binding across phase boundaries. Here, we present computational results that explain how preferential binding of ligands to scaffold molecules in different phases can impact phase separation and the compositions of dense phases. We show that phase separation is destabilized by monovalent ligands. In contrast, multivalent ligands, depending on their mode of binding, can stabilize phase separation by serving as crosslinkers that network scaffold molecules. We also find that concentrations of scaffolds within dense phases are generally diluted by ligands. This arises because ligands destabilize condensates by preferentially binding to scaffolds in the dilute phase or because ligands have to be accommodated within dense phases when they bind preferentially to scaffolds in the dense phase. Importantly, we show that partition coefficients, which are routinely used for compositional profiling of condensates, say nothing about the regulatory impact of ligands on the phase behavior of scaffolds. Therefore, instead of measuring partition coefficients it becomes imperative to measure how ligands impact threshold concentrations of scaffolds. These measurements, performed as a function of ligand concentration, will help with understanding the regulation of condensates and enable the design of molecules that impact condensate formation or dissolution.