That would be a bad idea.
1) You don't want to mix thermal compounds, as it is unclear how they would interact
2) The amount required is as little as possible to fill small gaps between the CPU heat spreader and CPU cooler. More is actually worse and begins to act as an insulator.
If you want to use your own compound, completely clean the pre-applied compound with isopropyl alcohol and a lint free cloth (heavy duty paper towels, cotton swabs or pads, or coffee filters are popular choices as well)