Yes, you can include alternative-specific constants (ASCs). In our software it will often be estimated as the utility of the attribute upon which the alternative-specific effects depend (e.g. brand or transportation mode).
On occasion, for particular design situations (e.g. when I have more than one constant fixed alternative), we need to add ASCs manually. The power trick here is to export your design from our software as a .csv file, Then work in Excel to add columns to the design to capture the ASCs of interest. You can then import your customized design into our stand alone CBC/HB software, use menus within the software to make sure your ASCs are properly coded (typically by identifying them as "user-specified coding") and then you can run your models.