I think the answer is that this is possible, and one way to do it is as follows:
1. Generate a partial profile design with the partial profile attributes and alternatives.
2. Export the design and manually add an additional attribute, containing one level for each partial profile alternative, and additional levels for each constant alternative.
3. Specify the partial profile levels to be 0 for the constant alternatives.
4. Copy your CBC.ssi file and change the design to match the one you are going to import.
5. This means adding your new attribute, and changing the design to be alternative specific.
6. Test your design using the advanced test to make sure you have good standard errors.
This is what I have done, and I think the process is the right one to do.
Clearly this approach only works when one is happy with the realism of respondents comparing the partial profile alternatives to the constant alternatives.
If anyone has any comments to add please let me know!