Yes, MBC models can involve options on the menu that don't change price. But, the software requires that every model you build include at least one independent variable (beyond the alternative-specific constants). There are two ways around this:
1) Choices of fixed alternatives on the menu are often significantly affected by prices of other items on the menu (as cross-effects), so you can specify certain other cross-effects that are significant.
2) Often times in MBC modeling you want to collapse the choice of multiple (synergistic) alternatives into a single dependent variable with a greater number of levels (we call these "combinatorial dependent variables" in the documentation). When you implement combinatorial coding of the dependent variable that involves some options that have price variations and some that are fixed alternatives, there will certainly be some independent variables (such as price variations) that you will specify in the software to get around the restriction that all models must have at least one independent variable.