Assuming you are in the US (sorry if I'm wrong, but you didn't specify!), normal WiFi falls under Part 15 regulations which limit the radiated field strength, not the transmit power. This means that, assuming the transmitter is not underpowered, you cannot legally increase the range using directional antennas.
Supposing you did so anyway, hooking up multiple directional antennas to the same transmitter will split the input power among those antennas, so you're back to where you started.
Here are your available legal options:
Make sure the WiFi AP you use actually transmits the maximum legal power and has an antenna with a suitable pattern. (In particular, a so-called “high-gain omnidirectional” antenna will radiate mostly in the horizontal plane and less in the "up/down" directions, which might be good for the range or bad if your terrain is not flat or the antenna isn't oriented properly.)
Use multiple APs arranged in a large circle. This only extends your range by the radius of the circle. (Multiple APs in the same location would increase the total power radiated but not in a way useful for communication since they're not coordinated.)
Obtain an amateur radio license, which will allow you to transmit more power. The 2.4 GHz ISM band used by WiFi overlaps with an amateur radio band, so you can use stock WiFi equipment together with directional antennas and/or power amplifiers, provided that you:
- include your assigned callsign in the SSID
- configure the device to use a channel which is in the amateur band, rather than autoselecting
I haven't done this myself, so I can't advise on the exact details of doing this, but it's fairly popular so you should be able to find information easily.
This does not require the other participants to obtain a license.