I'm not sure as to the legalities and/or ethics, but I have been involved in a few projects where the designer was also performing CM, and serious design deficiencies arose during construction... and it just depended on the company that was involved: firm "A" took great pains and probably lost a lot of $$$ to correct the problems, and firm "B" just denied, denied, denied... covered up and caused all kinds of problems.
So based on that, I would say that it's good to very carefully examine the laws and ethics rules in your state, and if they allow it, to very carefully think about whether or not you could handle the type of situation I have decribed. And research the company - actually check their references, and find out as best you can whether they are like firm "A" or more like firm "B". Assume firm "B" if you don't get a clear answer.