Liquid-liquid phase separation (LLPS) is thought to contribute to the establishment of many biomolecular condensates, eukaryotic cell structures that concentrate diverse macromolecules but lack a bounding membrane. RNA granules control RNA metabolism and comprise a large class of condensates that are enriched in RNA-binding proteins and RNA molecules. Many RNA granule proteins are composed of both modular domains and intrinsically disordered regions (IDRs) having low amino acid sequence complexity. Phase separation of these molecules likely plays an important role in the generation and stability of RNA granules. To understand how folded domains and IDRs can cooperate to modulate LLPS, we generated a series of engineered proteins. These were based on fusions of an IDR derived from the RNA granule protein FUS (fused in sarcoma) to a multivalent poly-Src homology 3 (SH3) domain protein that phase-separates when mixed with a poly-proline-rich-motif (polyPRM) ligand. We found that the wild-type IDR promotes LLPS of the polySH3-polyPRM system, decreasing the phase separation threshold concentration by 8-fold. Systematic mutation of tyrosine residues in Gly/Ser-Tyr-Gly/Ser motifs of the IDR reduced this effect, depending on the number but not on the position of these substitutions. Mutating all tyrosines to non-aromatic residues or phosphorylating the IDR raised the phase separation threshold above that of the unmodified polySH3-polyPRM pair. These results show that low-complexity IDRs can modulate LLPS both positively and negatively, depending on the degree of aromaticity and phosphorylation status. Our findings provide plausible mechanisms by which these sequences could alter RNA granule properties on evolutionary and cellular timescales.