Can you overcharge a capacitor with a lower voltage power source?
With a static voltage source, a capacitor in series will charge up until its voltage is the same as that of the source.

With a few components you can build a boost converter, which is capable of charging a capacitor beyond the voltage of the supply due to the inductor forcing more charge into the capacitor when the switch is open.

Operating a capacitor near its voltage limit can result in reduced capacitance though, and charging it past its limit may destroy it violently.