You can always switch brands; mineral to synthetic and reverse. Part of the oil development program is to test for general compatibility.
The only thing not to do is a 50%-50% mix of two oils, even same brand. A 5W-30 and a 10W-30 both from Mobil don't necessarily have the same additive package. The problem with mixing additive packages is that some additives only work at 100% effectiveness at 100% of the dose. They work at 40% effectiveness at 50% of the dose. You may have two oils, each contributing 50% additive, but resulting in only 80% of the performance.
And before anyone panics, when you change your oil the amount left behind is not enough to worry about. Don't go double flush your oil, a simple change is fine.