Well, such customized things cannot be done with the standard steps in SSI Web's CBC system...but they could be done with some fancier power tricks in SSI Web CBC.
First, you'd need to export a standard CBC design from the Design tab in your CBC project to a .CSV file. Within Excel, you can open that design file and do some modifications to it, such as randomly showing empty spaces for some of the positions on the shelf.
You'd probably make an "empty" attribute level for your brand attribute which is connected with Conditional Display tables to show empty for brand and price on the screen.
One problem with this approach, though, is that it still would be possible for respondents to select the "blank" concepts, since radio buttons would still be shown beneath those concepts. I don't know if there is a way to trick SSI Web into not showing radio buttons beneath empty shelf concepts. Maybe one of the tech support gurus has a tricky CSS solution for that?
If all that fails, then you could think about building a fancier Free Format CBC exercise in SSI Web that conditionally shows the radio button or not based on whether a blank is to be displayed in that concept position. I know such a thing could be done with some Perl script.
When modifying .CSV design files by hand to accomplish certain customized designs, make sure to re-import the design into an SSI Web CBC project (with the new attribute level list dimensions of your modified .CSV file) and then make sure to perform the "Advanced Design Test" in CBC...generated simulated respondent data and checking the standard errors of your aggregate logit coefficients. The rule of thumb is to have 0.05 or smaller for standard errors of main effects and 0.10 or smaller for standard errors for interaction effects.