Perhaps others have ideas for this, but the solution I'm aware of is to treat your CBC study as an alternative-specific design (described in the documentation). Typically, alt-spec designs are used in cases like trading off bus, car, train, walk, and "other". These five alternatives are specified as 5 levels of the first (primary) attribute. Then, bus attributes are associated with the "bus" level of the primary attribute. Car and train attributes are associated with their levels of the primary attribute. The Walk and "Other" categories might not have any attributes associated with them, so they look like two fixed "None" alternatives on the screen that respondents can choose among.