Sorry, but I have to say I'm confused about your questions.
First, our CBC software always keeps track of which attributes were shown in each task, so there is always common coding (managed by the software) within our system. My guess is that's probably not what you meant.
Next, if you want some attributes (such as brand and price) to always be shown, but other attributes to rotate in, then you need to leave Brand and Price to be either at the top of the concept, at the bottom of the concept, or top (Brand) and bottom (Price). Then, the middle attributes are rotating in and out of the task.
Regarding dropping levels of attributes per person, that's something that the ACBC software can do (with its ability to use constructed lists of attributes and attribute levels), but CBC is not able to do automatically.
Now, it is possible to trick CBC into showing a customized (say) 5 out of 10 possible brands, using a constucted list and showing each of 5 list elements as the attribute level text...but you'd have a nasty data processing project on the back end to unravel what happened and deal appropriately with the missing levels for utility estimation.