Tomabowen: So glad you posted. You do NOT need multiple permits for overnight backpacking on the Mt Whitney trail. The ONLY permit you need is for the date you start up the trail.
Overnight permits are good for the entire summer (or 14 days if you stay in one spot). The most important rule is that you ENTER on the entry date on the permit. It is good as long as you don't exit the wilderness for 24 hours, and exit/re-entry must be on the same trailhead.
I posted a response to your Shout Box question yesterday here:
Misc Questions. In fact last time I checked, there was a single permit available to enter on the Saturday you are asking about.
It is highly likely that when you go to the Visitor Center (just S of Lone Pine) to pick up your Sunday permits, that there will be slots available for Saturday, so you could just swap the permit for Saturday. In fact, if you want to change from a Sunday to Saturday entry date, I think you need to call the Wilderness Permit number and talk to the rangers there: 760-873-2483. I think they can change the dates without your incurring additional cost.