transfer function of a complicated circuit
You can use the fact that you are dealing with a linear system.

The overall transfer function H(s) = H1(s) + H2(s)

where H1(s) = Vout / Vin1, Vin2=0 and H2(s) = Vout / Vin2, Vin1=0

Assuming an ideal OpAmp with infinite gain one of the capacitors is between 0 (=gnd) and the virtual ground of the OpAmp and can therefore be ignored for the calculation of H1 and H2.