My “floor guy” was here today so I asked him. He said the engineered floors he just put in our living room could be refinished 4 or 5 times, if done by a competent refinisher. I’m sure different products might have different tolerances. Ours look identical to the solid wood we have in other parts of the house, and should have less warping problems.
Solid hardwood flooring is available pre-finished, too. I have prefinished solid oak flooring in my living room and dining room. Parts of it get a lot of sunlight, causing the stain to fade a bit after 15 years. I may sand it and refinish it at some point.