I recently resized some 286 grain .366 bullets to .358 for my Whelen with a Lee sizer. I had to do it in two steps, with a .361 die as the middle-man. I have a Lee turret press; a stouter press may have been able to do it without the .361 die. 0.003 should be easy in one pass, on any press. I used both Hornady One-shot and Lee lube. I didn't notice a different between the two.
Reduction in stages is best to retain bullet integrity. 0.003 to 0.004 inches maximum in one pass is considered optimum to preserve bullet/jacket integrity and overall shape. No more than 0.008 total reduction. Generally speaking short, fat bullets show the least damage when reducing their diameters. Once upon a time, this was popular with RNs. for example, reducing .323 bullets to .318 for Commission rifles. In Canada and the UK, reducing .313 bullets to .308 diameter was done when when .313 bullets were everywhere.
When it comes to deformation, spitzers and BT spitzers are the worst offenders. They can bend like bananas if too much reduction is attempted in one pass. Even a 0.004 inch reduction can cause the core to come away from the jacket. I had the most problems with Sierra bullets. IMO, this was due to their thinner jackets.
Necessity often demands reduction, but if it is going to be a regular thing, it's best to use two or three dies. If possible, no more than 0.010 inches total. CH4D can produce inexpensive dies for the purpose.