Can an immunized witness testify before a grand jury?

The function of the grand jury is to inquire into all information that might possibly bear on its investigation until it has identified an offense or has satisfied itself that none has occurred. As a necessary consequence of its investigatory function, the grand jury paints with a broad brush.... United States v. R. Enter., Inc., 498 U.S. 292, 297, 111 S.Ct. 722, 112 L.Ed.2d 795 (1991) (citation omitted). Given the importance of the grand jury's investigative role, there is no reason to permit an immunized grand jury witness to obstruct the administration of justice by endeavoring to influence or impede the grand jury's investigation. It would appear that if there was ever a moment for a witness not to engage in obstructive testimony, it would be before a grand jury.