There seems to be a misunderstanding of how these RFID cards work, not only in this posting but others too. Increasing the RF output power will not necessarily increase the range, it will extend how far the modules signal will reach but not that of the card/tag it's talking to. They work by 1. Powering the internal circuit of the card 2. Sending commands/data to it and 3. Allowing the card/tag to modulate the loading on the antenna. The loading is then analyzed by the module to recover the data from the card/tag. If you simply add a power amplifier it will only increase the range of steps 1 and 2 but it will almost certainly prevent step 3 from happening at all.
You can experiment with physically larger antennas, it will help to some extent but you have to keep them tuned to 125KHz. In most modules there will be some status indication that alerts you to an antenna problem. The actual 125KHz frequency is determined by the module, not the antenna and is of course fixed in the card/tag anyway.
Brian.