No, you cannot over-press tofu in general. Now - the amount of moisture does affect the texture, so if you are going to want a softer texture, then you can over-press it. Tofu is a very versatile ingredient that can be used in many different dishes (and is a great replacement for meat, especially breakfast meats). If you are looking to have a firmer texture, pressing the tofu is a great way to achieve that. By using a tofu press you can be sure that the tofu will be evenly pressed and will have a more consistent texture.