How can I increase the multiplier of a voltage doubler circuit using IC4049?
If you connect a second one like this:







simulate this circuit &ndash; Schematic created using CircuitLab

(only one oscillator is required, so you can use all the inverters in the second chip in parallel if you want). 

You'll get about -5V, so the difference between the two will be about 15V.. that will allow you to connect more LEDs in series.  

You might want to put reverse biased diodes across each of the two output capacitors, your C3 and my C2.