As far as different brand of oil is concerned, it should not be a problem at all as long as the grade is the same or has a lower end viscous point but never should go for a higher end viscous point. Eg: If 20W50 is recommended, you can use 10W50 but never should use 10W40 or 20W40 because the 50 is the grading for the higher temp vicouscity. Read this for a better understanding: Motor Oil Viscosity Grades Explained in Layman's Terms
Coming to synthetic oils. From what I have undetsood reading various sources is that for Wet Clutch boxes, it is never recommended to have synthetic simply because it might end up slipping the clutch due to the extermely fine/smooth nature of synthetic. Mineral oils have enough abrasive mineral particles in them that they niether harm nor slip but provide the requisite lubrication. An oil is supposed to aid in engine break-in by letting the components shave some metal debris off each other so that they fit perfectly and work harmoniously. Synthetic oil during break-in period is "khud ke pair me khulati marna"



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