How to identify 2-inputs 2 outputs transfer function matrix

Dear colleagues,

Kindly support me in finding the best efficient way to identify MIMO transfer function matrix of an HVAC system whose block diagram is attached. I can get an accurate responses for various inputs values applied on the input ports.

What is remaining for me is to identify the trnasfer function matrix to enable me applying INA multivariable control technique

The two inputs I have are the voltage of the blower fan and the mass flow of the refrigerant in the refrigeration cycle, while the outputs are the temperature of the zone (air-conditioned space) and the temperature of the mixed air entering the air handling unit

I am familiar with using the system identification toolbox of MATLAB to identify the SISO transfer function but I seriously face trouble in how to find the transfer function matrix of 2-inputs 2-outputs.

Kindly advise and support.

Regards

Basim Touqan