1999 Chevrolet Cavalier coupe transmission?

[KibopK]

I have a 1999 Chevrolet Cavalier, the owners manual says to use Dexron -III Transmission fluid the transmission has a new transmission in it, it doesn't say don't use any other fluids, but it also doesn't say its fine to. I want to put all synthetic oils in my car Engine Oil, transmission oil, power steering, brake fluid, everything. I know i dont need to but i want to. So is it ok to use a different transmission oil in my car? i want to keep the transmission in top notch condition so using full synthetic oil would be the best thing i can do for it and shifting nicely. So is it ok to use different transmission fluid than the owners manual has in it?

[pedro7of9]

USE DEX 3,,,EXCUSE ME FOR YELLING BUT USE DEX 3