For frying, I usually use a mixture of olive oil and butter. The oil slows down the process of the butter burning. It's certainly not as good as ghee, but ghee tends to make stuff greasy.
If you put butter into a pan that is too hot and it starts burning, it can be useful to cool things down by adding some oil. But the milk solids will always burn at a given temperature. A mixture of olive oil and butter won't let you cook at a higher temperature than just butter.