The system you have mentioned is fully controllable as the controllability matrix has full rank. By 'rescaling' I assume you want to control the system's step response. You can easily do that by using a feedback control. In this case a positive feedback control is going to make your system unstable. So you have to use a negative feedback controller. Something like this:
A=[0,1,0,0;0,-42.44,212.24,0;0,0,0,1;0,0,0,-42.44];
B=[0,0;106.12,-5;0,0;78.6,-42.44];
C=[1,0,0,0;0,1,0,0;0,0,1,0;0,0,0,1];
D=[0];
system=ss(A,B,C,D);
step(system) % Step response of original system
hold on
k=[10 10 10 10; 10 10 10 10]% This is a dummy gain matrix.Put your gain matrix here.
system1=ss(A-B*k,B,C,D) % Closed loop system with negative feedback
step(system1) % Step response of closed loop system
