Yes, you can though storing definitely depends on the tofu type. Silken can be stored in an airtight container filled with water and will keep in the fridge for a couple of days. Firm Tofu can be stored in the fridge and freezer. Same way to keep firm tofu as silken tofu and also the firm tofu can be stored in the freezer. Remove excess moisture with kitchen paper towel, then keep it in a ziplock freezer bag. Thaw out at room temperature wrapped in kitchen towel paper for this will absorb moisture. Cut it into small pieces and you can use it for miso soup ingredients, or into sukiyaki etc. It will keep about a month in the freezer.