It's been demonstrated that upscaling incrementally improves image quality, Empirical Study: Extreme digital upscaling, and that thread also shows that choosing 105% increments versus 110% increments can produce different results.
It's pointed out by Stan Rogers in this thread How to scale up a photo? that
for users of Ps CS6 (and, I'd assume, above when there is an "above"): the resize options now include a "Bicubic Auto", which does the smoother/sharper thing automatically depending on the new resolution, and does iterative up-rezzing so you don't have to do it manually anymore.
What type of iterative up-rezzing is "Bicubic Auto" doing when it upscales, and is there a way to control this? Such as 105% versus 110%?