There are private institutions that conduct their own investigations, however, the cost for these organizations are much higher than sticking with a public background check.

Here are some tips to get you started
Be sure to obtain permission in writing from the person you wish to conduct a background search on. Let them know which types of searches you will be conducting ; i.e., criminal background check, employment verification, education, etc. the types of searches you will be conducting should be listed on the permission form that you ask them to sign.
Give the search engine the personal information that is needed, including a first and a last name, the person's date of birth, mailing address, and social security number.

Pay for the cost of your search. Complete all of the required forms, making sure that you pay close attention to the submission requirements. Some agencies will ask you to send in the form or forms in together along with your address and a stamped envelop. They may also ask you to include a check or the money order for the processing fee.