Since you say Junction Meadow does that mean you plan to do the High Sierra Trail and then further and you need resupply?
I think the Whitney Portal Store might hold a package for you but still your only option is to go down to the trail head and get it.
Resupply is a tricky business I have always found and often dictates my route planning due to it. I have been lucky enough in the past to have family members bring me packages or cache them or I once left a cache in the Onion Valley Trailhead bear boxes.
