Is it possible to boost current into a load without boosting voltage also?
Along with P = V * I you also need Ohm's Law which states that V = I * R. In the case of a resistive load the voltage and current are proportional. The only way to increase the current is to increase the voltage.

The answer, therefore, is no.

Note that since V and I are proportional that power changes with the square of the voltage or current. So if you drop your voltage to 90% the power will go down to 81%. (0.90 * 0.90 = 0.81.)

Will you get satisfactory performance at 81% power? It depends on the device. A heater might work OK although it will take longer to heat the room. An electronic device may not operate. A motor may not have enough torque to start.