Those sorts of tricks are accomplished using "Customized CBC Questions Using Free Format". It's described in the section in the CBC Help called "Advanced Designs."
Using Free Format CBC questions, you can write your own custom HTML to show the CBC tasks. I'd Preview a standard CBC question and "borrow" that HTML to display your own custom CBC question.
[Or, you can just "cheat" by using standard CBC questions (not Custom HTML) and just adding another grid-type question beneath the standard CBC question (to ask for chips for the long haul flights).]
For the Free Format CBC questions, the instructions in the manual assume you'll read assume only one vector of chips (for one occasion). Go ahead and follow the instructions so that the first vector of chips is automatically recorded as if CBC software had done it. But, you'll want to develop a second CBC dataset with the second vector of chips, for estimating a separate set of utilities. Just "trick" SSI Web into thinking that you are doing this second CBC project as paper-and-pencil mode. Format the responses to the second vector of chips in a .csv file using Excel. Create a copy of your SSI Web project (using the File + Save As). Then, in the copy of the SSI Web project, use the paper-and-pencil import to bring in those "paper" respondents who answered the second vector of chips. This creates a second CBC data set for you to analyze the part-worth utilities applying to the second occasion-based condition (the long haul flights instead of the short haul flights). We have documentation on conducting paper-and-pencil surveys that you can follow.