Generally the private sector is more effective than government. However, enforcing taxes is one thing that shouldn’t be privatized.
The historical record on this matter is extensive, including research from Cambridge University detailing the tyranny and corruption associated with private tax enforcement in ancient Rome. Yet, under new regulations arbitrarily dictated by IRS, private contractors are actively participating in tax audits. President Trump has stated his commitment to regulatory reform and "draining the swamp." This should be an obvious place to start.
There are three reasons why private companies shouldn’t conduct audits. First are the conflicts of interest. Private firms conducting audits gain access to the books of other companies. This risks these firms selling secrets or using what they learn to gain a competitive advantage. Think of it as legalized corporate espionage.