They make RGB LED amplifiers. I haven't had the chance to test them, but they seem suitable for your application. You just take the end of your current LED strip and connected to the input side, then you connect your extra LEDs and a power supply to the other end.
It's best to stay away from the max amperage of anything, I usually don't get within the 1A range when it comes to large power draw.
Edit: I found one that seems more legit, clearer description: http://www.amazon.com/Signal-Amplifier-Range-Extender-Strip/dp/B0050CO6QW/ref=cm_cr_pr_product_top