Liberty Springs is not a big site - 7 single and 3 double tent platforms. It is built on the side of the mountain and the general terrain is quite steep, treed, and rocky, with very few places one could realistically pitch a tent. The good news is you're hiking in on a Sunday afternoon when the weekenders should be gone, but the bad news is getting there so late in the day with very few options. In my experience, the caretaker will double up smaller tents on the single platforms to fit people in, but even if they fit you in your group may get separated. I've seen evidence of a few "stealth" sites (obviously not all that stealthy) further up the trail near the ridge (see this thread as well http://www.whiteblaze.net/forum/show...-in-the-Whites ), but I wouldn't suggest nor rely on them as I haven't been up there since Oct. 2012 myself.