The formation of domains in multicomponent lipid mixtures has been suggested to play a role in moderating signal transduction in cells. Understanding how domain size may be regulated by both hybrid lipid molecules and impurities is important for understanding real biological processes; at the same time, developing model systems where domain size can be regulated is crucial to enable systematic studies of domain formation kinetics and thermodynamics. Here, we perform a model study of the effects of oil molecules, which swell the bilayer, and line-active hybrid phospholipids using a thermally induced liquid-solid phase separation in planar, free-standing lipid bilayers consisting of DOPC and DPPC (1,2-dioleoyl-sn-glycero-3-phosphocholine and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine, respectively). The experiments show that the kinetics of domain growth are significantly affected by the type and molecular structure of the oil (squalene, hexadecane, or decane), with the main contributing factors being the degree of swelling of the bilayer and the changes in line tension induced by the different oils, with smaller domains resulting from systems with smaller values of the line tension. POPC (1-palmitoyl-sn-2-oleoyl-glycero-3-phosphocholine), on the other hand, acts as a line-active hybrid lipid, reducing the domain size when added in small amounts and slowing down domain coarsening. Finally, we show that despite the regulation of domain size by both methods, the phase transition temperature is influenced by the presence of oil molecules but not significantly by the presence of hybrid lipids. Overall, our results show how to regulate domain size in binary membrane model systems, over a wide range of length scales, by incorporating oil molecules and hybrid lipids.