Yes, yes you can. However, there is a law of diminishing returns when it comes to how many generations out from the F1 generation you go with your yeast. Yeast loses it's vigor and starts to show signs of problems around the F5-F7 generation when, through natural reproduction, differences in the yeast DNA begin to appear to such an extent that they exhibit different characteristics than the F1 generation (petite mutants, etc.).
In brewer's english, that means you can re-wash the yeast about 5-7 times before you start to notice differences in taste or have problems with things like stuck fermentations due to a loss in vigor.