The transfer function of a linear system is measured through an AC analysis. Any SPICE simulator will perform this analysis. From the magnitude and phase response (or equivalently real and imaginary voltages), you have your complete transfer function in graphical form. I typically export this into MATLAB for further analysis when needed.
There are many known methods that can take a graphical transfer function and estimate the poles/zeros. Prony, Levinson-Durbin, etc. See Modern Spectral Estimation by Kay.
Alternatively you can perform a pole-zero analysis and SPICE will derive the poles and zeros in the transfer function. I assume it works by applying one of the common spectral estimation methods to an AC analysis. You do have to manually filter out the poles at infinity, though. It sounds like this is what you are after.
SPICE is a numerical simulation that solves ODEs using a variety of methods. Multisim provides you with a way (in my opinion a very good way) of quickly designing or analyzing analog circuits provided you give it the right models. What you are describing is performing a Laplace transform analysis on a circuit, which SPICE does not do as far as I understand it. For simple circuits, this is easiest to do by hand, in MATLAB, or Mathematica.
-J
