No. "Disqualified Persons" may not be Qualified Intermediaries. With limited exceptions, a Disqualified Person is any party who has acted as your agent, employee, attorney, accountant, investment banker/broker, or real estate agent or broker within the two-year period ending on the date of the first transfer of any relinquished property. Also disqualified are the family members of Disqualified Persons, as well as partnerships, corporations and other entities in which you, or your related party, own directly or indirectly, more than a 10% interest.
Example: Your attorney owns 11% of the stock in his law firm, and his wife owns her own intermediary firm. You wish to use his wife's intermediary firm as your Qualified Intermediary. If your attorney has done any work for you in the last two years, other than strictly I.R.C. Section 1031 tax-deferred work, his wife's firm is "disqualified" to act as you Qualified Intermediary. Conversely, if ten law firms each own 10% of a corporation organized to act as a Qualified Intermediary, you could use that Qualified Intermediary even though your law firm was one of the ten owners.