Classic STP (aka grandpa's motor honey) is a viscosity improver, often used in past if engine is old and oil pressure too low. But it can cause carbon-packing in the ring grooves. My dad used it mostly for lubing fired rifle shell cases before running through the resizing die (before tungsten carbide reloading dies).

It seems to me that adding a thicker lube to Singer oil is like the proverbial adding vegetables to stone soup. Gear lube... wax... anything like that and you don't need the Singer oil. It's a nice light lube. If you want something as light but with greater chain durability and not the hassle of melted wax, I think as noted above there are homebrew recipes with wax dissolved in a light solvent to drip on. But I don't know if those work as well as melted wax; My perception (could be right or wrong) is that the wax melt, once solidified, forms a rigid cylinder between rollers and side plates and pins. I don't know if thinned wax will have similar adhesion to the parts.