A party to an administrative agency investigation does not have a constitutional right to be accompanied by counsel during such proceedings[i]. In Anonymous v. Baker, 360 U.S. 287 (U.S. 1959), the court held that a witness examined in a state investigation conducted in private is not constitutionally entitled to the assistance of counsel while being interrogated.
However, in criminal proceedings a party to the proceeding should be afforded with an opportunity to secure counsel of his own choice[ii]. In United States v. Steel, 238 F. Supp. 575 (S.D.N.Y. 1965), the court held that a party to a proceeding should be afforded a fair opportunity to secure counsel of his own choice, but this is in a criminal prosecution and in a constitutional context. The court further held that even in such cases, there can be reasonable limitations on the selection of counsel.
Thus, a party has no constitutional right to be accompanied by counsel during administrative proceedings.
[i] Finance Com. of Boston v. Mayor of Boston, 370 Mass. 693, 697 (Mass. 1976)
[ii] Matter of Comprehensive Investigation of School Dist. of Newark, 276 N.J. Super. 354 (App.Div. 1994)