Can you increase the input impedance.?
The answer is ... it depends what else you want to achieve.

Increasing all the resistors will increase the input impedance. 

The limit starts to come in where the transistor loses gain at very low currents. 

As R4 is dominating the circuit as drawn (assuming reasonable hFE like 100 or so), sorting R4 will give you the most bang for buck.

In order to increase the AC input impedance, without disturbing the DC bias, you could bootstrap R4, by splitting it into two parts, say two 5k resistors in series, and connecting a capacitor from Q1 emitter to the mid point. As Q1 emitter follows the base with a gain of 0.99ish, that will all but eliminate the signal current that gets conducted down R4.

With R4 bootstrapped, R3 now dominates. You could replace R3 and R4 potential divider by a single resistor from a point of the right voltage, bootstrapped to Q1 emitter. That eliminates R3 and R4 for signals.

Replacing Q1 with a darlington transistor for much higher hFE will reduce the R2 term.