Endogenous biomolecular condensates, comprised of a multitude of proteins and RNAs, can organize into multiphasic structures, with compositionally-distinct phases. This multiphasic organization is generally understood to be critical for facilitating their proper biological function. However, the biophysical principles driving multiphase formation are not completely understood. Here, we utilize in vivo condensate reconstitution experiments and coarse-grained molecular simulations to investigate how oligomerization and sequence interactions modulate multiphase organization in biomolecular condensates. We demonstrate that increasing the oligomerization state of an intrinsically disordered protein region (IDR) results in enhanced immiscibility and multiphase formation. Interestingly, we found that oligomerization tunes the miscibility of IDRs in an asymmetric manner, with the effect being more pronounced when the IDR exhibiting stronger homotypic IDR interactions is oligomerized. Our findings suggest that oligomerization is a flexible biophysical mechanism which cells can exploit to tune the internal organization of biomolecular condensates and their associated biological functions.