You must use a DC-boost converter to increase the voltage (since capacitor will give 2.7 maximum). There are very easy circuits (just with a transistor, a comparator, an inductor and a capacitor) which switching the mosfet and charging the inductor will generate a higher output voltage. That doesn't mean free energy, although these circuits are very efficient the output power will be (ideally) equal than the input power, so if the voltage increased then the current would have.
But the question is, what driver circuit could you supply with such a low voltage?