There are sixteen to twenty authorized sites within the hiker-in area. There are also some stealth site that people use when the campground is full.
There is usually a big turn over at the WP Hiker-in area, so if you do not get a site the first night, you will get one the second.
Also, the family campground holds back sites for walk-ins. See the campground manager for one of those. This is your best option for a multi-night stay.