As Kees says, if the internal audits are not working and, as Tom also makes a very good point about the extra cost, it would be far less burdensome and get the same kinds of results in improvements if you fixed the internal audit process!
Doing another audit program - for nothing - will fail to address the real issues and cost you $$$. Also, just because someone asks you for it, unless it's part of a contractual arrangement, these things get very out of control and you'll end up doing more and more for nothing.
Tell us how often etc these processes are reviewed by your IA program. When do you plan them, what info do you use to plan the, against what audit criteria do you conduct the IAs?