Filter Z Transform Manipulation

Hello,

I usually design filters using the filterDesigner and then export its coefficients to the workspace to use in the script. However, now im trying to manipulate the filter I have. What i pretend to is I have a Low Pass filter and i want to observe what happens when I do H(z^2) or something like (0.1(1-z^-1)H(z)). How can i plot this having the original filter coefficients?

Thank you

EDIT: I've tried this:

freqz(test.Numerator.^2,1);
z = tf('z'); 
H = tf( 0.1 - 0.1*z^(-1), 'Variable','z^-1')
freqz(H*test.Numerator,1)

However i believe its far from correct and the last one simply doesn't work...