In short, it is possible to combine synthetic oil with conventional oil, provided you do so only in the right amounts. Synthetic oil is far superior to conventional oil at a molecular level. It has a higher viscosity rating and is more efficient in both warmer and colder temperatures. You must use the proper ratio between synthetic and conventional oils. Otherwise it could have a negative effect on your engine.
Mixing Synthetic and Conventional Oils
Firstly, there is no mixing of the two types of oil. Synthetic oil bonds better to moving parts, and conventional oil is not able to penetrate the synthetic layer. If you mix half synthetic with half conventional, the oil pump will still be operational, but it will be akin to running your engine on only half the amount of oil.
The proper ratio is approximately 3 parts conventional to 1 part synthetic. This will allow your engine to enjoy the benefits of both types. It is important, though, to make sure that the oil weights are identical when blending a combination of the two.