Yes you can increase the power - lots of kits make that claim. I recommend that you carefully understand regulations as they apply to your situation.
Note that the output of a simple FM transmitter may not be clean - it is likely to contain a lot of junk on other frequencies. At low power it's of little consequence. Whatever method you use to boost the power will boost the junk too unless you address that in your amplifier. While not rocket science RF circuits may be a bit much for the inexperienced.
Don't let someone talk you into thinking that no one enforces the regulations. Many of the people I know in the area make their living in the communications business- commercial radio, TV, military. They spend some of their time tracking down faulty transmitters or other sources of RF - not because it's against the rules but because it's fouling up their legal and licensed operations and costing them money. They won't hesistate to notify the authorities.
Please pardon the lecture but we get a lot of posts here about boosting power of transmitters.