gmacfarlane has been very clear. But to be more precise, and I assume you perform a cross section analysis, the core assumption is the IIA (independence of irrelevant alternatives).
You can not force your data fit into the IIA assumption, you should test it and hope for it to be satisfied. SPSS could not handle the test until 2010 for sure. R of course does it, but it might me easier for you to migrate to Stata and implement the IIA tests provided by the mlogit postestimation commands.
If the IIA does not holds, mixed multinomial logit or nested logit are reasonable alternatives. The first one can be estimated within the gllamm, the second with the far more parsimonious nlogit command.
