Yes, you can safely mix one brand of oil (e.g. Pennzoil) with a different brand (e.g. AMSOIL) or conventional oil with synthetic oil (in fact, that’s what a synthetic blend is). Most synthetics today are fully compatible with conventional oils and can be mized.
However, just because you CAN it doesn’t mean that you SHOULD. Let me explain what I mean.
As an example, even though AMSOIL motor oils are totally compatible with conventional and other synthetic motor oils, mixing AMSOIL oils with other oil brands or types will shorten the oil’s life expectancy and reduce their performance benefits. AMSOIL does not support extended drain intervals where oils have been mixed.
The base oils and additives that make up an 'oil formulation' are carefully selected by the oil companies and blended together in a way that ensures that the finished product achieves the desired effect that they set out for it to achieve. The various additives in the ready-formulated oils are coordinated to each other and are properly proportioned.
Each oil company has its own unique 'proprietary oil formulation' for each of its various brands, types, and grades of oil; which in turn is different than another company's oil formulation for its various brands, types, and grades of oil. Any manipulation of this formulation has the potential to be harmful.
For instance, AMSOIL uses one type of 'base stock' (usually a blend of 2 or more base oils) for its top of the line Signature Series formula, adding its own specifically selected 'additive package' to it. However, it uses different base oils and/or a different 'additive package' for its XL Series and OE Series formulas.