OK, this will not foul up the experiment, but it will cause some headaches for you to do proper analysis. Explanation below.
Let's imagine you have 5 attributes, with levels as follows for the five attributes 2x3x2x3x3, where we assume price is the last attribute with 3 levels.
That means there are 2x3x2x3x3=108 possible combinations to show respondents. Approximately 1 out of 36 combinations shown to respondent will be of the magic "bob" concept, where you have to fix the price.
So, you should use conditional pricing (n-way pricing) where price is conditional on the combinations of the 4 other attributes. I'm assuming you'll be letting price just take on 3 values (the main effect of price) for all of the 108/3-1=35 product combinations. But, when "bob" concept appears, it will always show the same price for all three price levels. Go ahead and fill out the 108-cell conditional pricing table to reflect that fact.
Now, the headache comes during estimation, where you will need to do some custom coding of the data file and will need to fit a linear or log-linear term to price to fit the data correctly.
You'll need to export the CBC data to a .CSV format. From Data Management area within Lighthouse Studio, add a Job (Add Job...). Select Add button, and click "CBC (.csv, .cho)" format. Under File Format on that same dialog, click "Single Format .CSV". Export the job.
Now, open the .CSV file that was exported from the above in Excel. You'll see a column for the Price variable which currently takes on 3 states (1, 2, or 3). You'll need to write a few formulas in Excel to replace price with the actual price shown to respondents for each concept. And, when concept "bob" is shown, you'll need to fill in that constant price.
Save the modified .CSV file so that the Price column now contains the actual prices shown to respondents rather than 1, 2, or 3. (See more info below regarding scaling these prices for proper HB convergence!)
Now, I'm assuming you'll be doing HB estimation, so you'll need to estimate the part-worth utilities using the standalone CBC/HB Module (rather than Lighthouse Studio, which cannot handle "user-specified" prices) that you can download from: http://www.sawtoothsoftware.com/support/downloads/download-cbc-hb
But, prior to using the standalone CBC/HB Module to estimate the part-worth utilities, you'll want to make sure you have scaled the prices that you inserted to lead to proper convergence in HB. We have found that the prices should not exceed a range of about 1 to 10 to lead to proper convergence. So, if your prices shown to respondents ranged from 5000 to 10000, then you should divide all the prices in the Price variable column of the data file by 1000, leading to prices ranging from 5 to 10. Decimal places of precision are supported, of course.
The procedure above will lead to a linear estimation for price once you've set up the HB run properly in the standlone CBC/HB module. To do this, open the modified .CSV file in the CBC/HB Module. On the Attribute Information tab, click the drop-down control to change the Price attribute from part-worth to "User-specified". (This might already have been done for you by the system, when it recognized the decimal places of precision in the data file for the Price attribute.)
Be careful when you read the part-worth utilities plus the linear price coefficient into one of our market simulators that the market simulator recognizes the right price range that you used. You'll need to indicate to the simulator that the Price variable is a continuous variable. If you divided the prices by 1000 (for example) for estimation, when you specify the prices in the market simulator you will be specifying prices divided by 1000, or else the price coefficient you end up applying in the market simulator will be 1000x too sensitive.