I seriously doubt that the Broadcom chip outputs 1 Watt of TX power. The FCC limit is 1 Watt of conducted power into a 6dBi antenna. Since 1 Watt is 30dBm, the antenna gain accounts for 6dB of the 36dBm of transmitted power in the air, which is 4 times the power or 4 watts (36dBm EIRP). By the FCC rule, you cannot increase the 1 Watt of conducted power, even if you use a lower gain antenna. You can increase the antenna gain as much as you like so long as you do not exceed 36dBm EIRP. This may require backing off the conducted power. The price you pay with antenna gain, is that the higher the gain, the more directional it becomes.
The WiFi chips on the market either have low output power ~1mW, with the expectation of using an external power amplifier, OR some WiFi chips have internal power amplifiers and typically output around 20dBm or 100mW of power. The highest WiFi power found in power amplifiers in the market is 1Watt, but these use a lot of current, which is probably not happening on the TX1 board.
In the case of MIMO, the multiple power amplifiers must not add together to more than 1W of conducted power. If two power amplifiers are used, each outputting 20dBm or 100mW of power, then the total conducted power would be 23dBm (3dB is a doubling of power) which is 200mW (<1W conducted).
If two power amplifiers with 6 dBi antennas are used then the total power in the air, or EIRP, would be 29dBm (20dBm + 6dBi + 3dB = 29dBm, slightly less than 1W). To get to 36dBm EIRP, you would need antenna gain of 13dBi. Each power amplifier outputs, for example, 20dBm connected to a 13dBi antenna for a total of 33dBm in the air. With two such power amplifiers and antennas, you would double the power which adds 3dB for a total of 36dBi or 4 Watts EIRP. However, a 13dBi antenna is very directional and you would lose omni-directional coverage.