How to keep phase response of IIR filter?
To my knowledge, you can't linearize it arbitrarily, but that being said, you can obtain approximately linear phase by processing the output through a cascade of all-pass filters. 

An all-pass filter used this way is usually called a phase compensator or a phase equalizer. A single pole-zero all-pass IIR filter has the following structure
$$ H(z) = \frac{p - z^{-1}}{1 - p z^{-1}} $$
where $p$ controls the location of the pole/zero. You can optimize a cascade of filters of this type to equalize your phase response using least squares or some other filter design technique. 

Note that this technique reduces the primary advantage of choosing an IIR filter to begin with. Usually, the point in choosing an IIR filter over an FIR filter is to reduce computational complexity, so performing the phase equalization by cascading all-pass sections might result in a situation where using a linear phase FIR filter in the first place would have been more economical.