If you mean mixing with different types of the same fluid, almost all of them without any real ill effects. The only fluids that might be sensitive to mixtures are certain hybrid coolants and coolants that are incompatible with aluminum engine blocks.
Brake fluids? You can use whatever brand name fluid you have. The only difference is the DOT rating. DOT3 or DOT4-no difference in the way it works, just at what temperature it boils at. The higher the DOT spec-the higher the boiling point.
(Boiling brake fluid from overheated brakes causes brake fade.).
Motor oils are petroleum based
Power steering fluids are petroleum based but way thinner and have different additives than motor oil
Brake fluids are alcohol based (to absorb and contain moisture which damages hydraulic parts).
Coolants are alcohol based because they mix readily with water and lower the freezing point.
Transmission fluids are petroleum based and very similar to power steering fluids. In fact, GM used to recommend using Dexron trans fluid in their older power steering pumps.